LIMITED LIABILITY COMPANY AGREEMENT of HAYDEN GULCH TERMINAL, LLC

Exhibit 3.68

LIMITED LIABILITY COMPANY AGREEMENT of

HAYDEN GULCH TERMINAL, LLC

THIS LIMITED LIABILITY COMPANY AGREEMENT (“Agreement”) of Hayden Gulch Terminal, LLC (“LLC”), dated as of January 17, 2010, is made by Peabody Colorado Operations, LLC, a Delaware limited liability company (“Member”), as the sole member.

WITNESSETH:

WHEREAS, the LLC is a limited liability company formed under the Delaware Limited Liability Company Act (“Act”) pursuant to a Certificate of Conversion and Certificate of Formation filed with the Delaware Secretary of State on January 17, 2010;

WHEREAS, the Member is the sole member of the LLC.

NOW, THEREFORE, the Member hereby declares as follows:

1. FORMATION, NAME, PLACE OF BUSINESS, REGISTERED AGENT 1.1.

Formation of LLC; Certificate of Conversion

The Member hereby acknowledges the formation of the LLC as a limited liability company pursuant to the Act by virtue of the filing of a Certificate of Conversion and a Certificate of Formation with the Delaware Secretary of State on January 17, 2010.

1.2. Name of LLC

The name of the LLC as of the date of this Agreement is and shall continue to be Hayden Gulch Terminal, LLC. The business of the LLC may be conducted under any other name that is permitted by the Act and selected by the Member. The Member promptly shall execute, file and record any assumed or fictitious name certificates required by the laws of the State of Delaware or any state in which the LLC conducts business and shall take such other action as the Member determines is required by or advisable under the laws of the State of Delaware, or any other state in which the LLC conducts business, to use the name or names under which the LLC conducts business.

1.3. Place of Business

The LLC’s principal place of business shall be St. Louis, Missouri. The Member may establish and maintain such other offices and additional places of business of the LLC, either within or without the State of Delaware, or close any office or place of business of the LLC, as it deems appropriate.

1.4. Registered Agent

The street address of the initial registered office of the LLC shall be:

The Corporation Trust Company

Corporation Trust Center

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and the LLC’s registered agent at such address shall be The Corporation Trust Company. The Member may from time to time appoint a new resident agent for the LLC.

2. PURPOSES AND POWERS OF THE LLC

2.1. Purposes

The purposes of the LLC shall be to engage in any lawful business, purpose or activity authorized by the Member and permitted by the Act.

2.2. Powers

The LLC shall have all the powers and privileges as are necessary or convenient to the conduct, promotion or attainment of the business, purposes or activities of the LLC.

3. TERM OF THE LLC

The LLC shall continue until such time as it is dissolved pursuant to the Act.

4. LIABILITY OF THE MEMBER

Except as otherwise provided in the Act, the debts, obligations and liabilities of the LLC, whether arising in contract, tort or otherwise, shall be solely the debts, obligations and liabilities of the LLC, and neither the Member nor any director, manager, officer, employee, shareholder, controlling person or agent of the LLC or the Member shall be obligated personally for any such debt, obligation or liability of the LLC solely by reason of being a member or a director, manager, officer, employee, shareholder, controlling person or agent of the LLC or the Member. The failure of the LLC to observe any formalities or requirements relating to the exercise of its power or management of its business or affairs under the Act or this Agreement shall not be grounds for imposing personal liability on the Member, or any director, manager, officer, employee, shareholder, controlling person or agent of the LLC or the Member for liabilities of the LLC.

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5. CAPITALIZATION, MEMBERSHIP INTEREST AND DISTRIBUTIONS OF CASH FLOW AND CERTAIN PROCEEDS

5.1. Capital Contributions

The Member shall have no obligation to make additional capital contributions to the LLC.

5.2. Membership Interest

The Member shall own one hundred percent (100%) of the membership interests in the LLC, and all profits and losses shall be allocated to the Member.

5.3. Distributions

The Member shall decide whether and in what amounts the proceeds received by the LLC shall be distributed. All such proceeds, if any, shall be distributed one hundred percent (100%) to the Member.

6. MANAGEMENT AND OFFICERS

6.1. Member Management

Except as otherwise expressly provided in this Agreement, the business and affairs of the LLC shall be managed and controlled by the Member, and the Member shall have full, exclusive and complete authority and discretion to make all the decisions affecting the business and affairs of the LLC, and to take all such actions as the Member deems necessary or appropriate to accomplish the purposes of the LLC; and any actions taken by the Member shall be binding on the LLC.

6.2. Officers

a. Appointments. The officers of the LLC shall be chosen by the Member and shall consist of at least a President, one or more Vice Presidents, a Secretary and a Treasurer. Any number of offices may be held by the same person, except that the same person shall not be President and Vice President or President and Secretary. The Member may appoint such other officers and agents as it shall deem necessary or advisable who shall hold their offices for such terms and shall exercise such powers and perform such duties as shall be determined from time to time by the Member. The compensation of all officers and agents of the LLC shall be fixed by or in the manner prescribed by the Member. The officers of the LLC shall hold office until their successors are chosen and qualified, or until their earlier death, resignation or removal. Any officer elected or appointed by the Member may be removed at any time, with or without cause, by the Member. Such removal shall be without prejudice to the contract rights, if any, of the person so removed. Any vacancy occurring in any office of the LLC shall be filled by the Member.

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b. President. The President shall be the chief executive officer of the LLC, and shall be responsible for the general and active management of the business of the LLC and shall see that all orders and resolutions of the Member are carried into effect, and shall perform such other duties and have such other powers as the Member may from time to time prescribe.

c. Vice Presidents. In the absence of the President or in the event of the President’s inability to act, the Vice Presidents, if any (and in the event there be more than one Vice President, the Vice Presidents in the order designated by the Member, or in the absence of any designation, then in the order of their election), shall perfoun the duties of the President, and when so acting, shall have all the powers of and be subject to all the restrictions upon the President. The Vice Presidents, if any, shall perfoim such other duties and have such other powers as the Member may from time to time prescribe.

d. Secretary. The Secretary shall be responsible for filing legal documents and maintaining records for the LLC. The Secretary shall attend all meetings of the Member, and record all the proceedings of the meetings of the Member in a book to be kept for that purpose and shall perfoun like duties for the standing committees, if any, when required. The Secretary shall give, or cause to be given, notice of all meetings of the Member, and shall perform such other duties as may be prescribed by the Member or the President, under whose supervision the Secretary shall serve.

e. Treasurer. The Treasurer shall have the custody of the LLC funds and securities and shall keep full and accurate accounts of receipts and disbursements in books belonging to the LLC and shall deposit all moneys and other valuable effects in the name and to the credit of the LLC in such depositories as may be designated by the Member. The Treasurer shall disburse the funds of the LLC as may be ordered by the Member, taking proper vouchers for such disbursements, and shall render to the Member, at its regular meetings or when the Member so requires, an account of all of the Treasurer’s transactions and of the financial condition of the LLC.

f. Officers as Agents. The officers, to the extent of their powers set forth in this Agreement or otherwise vested in them by action of the Member not inconsistent with this Agreement, are agents of the LLC for the purpose of the LLC’s business, and, the actions of the officers taken in accordance with such powers shall bind the LLC.

g. Duties of Officers. Except to the extent otherwise provided herein, each officer shall have a fiduciary duty of loyalty and care similar to that of officers of business corporations organized under the General Corporation Law of the State of Delaware.

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7. INDEMNIFICATION

7.1. Indemnification

The LLC shall indemnify and hold harmless the Member, each director, manager, officer, employee, shareholder, controlling person, agent and representative of the LLC and of the Member (individually, in each case, an “Indemnitee”) to the fullest extent permitted by law from and against any and all losses, claims, demands, costs, damages, liabilities (joint or several), reasonable expenses of any nature (including reasonable attorneys’ fees and disbursements), judgments, fines, settlements, and other amounts arising from any and all claims, causes of action, demands, actions, suits or proceedings (unless asserted by the LLC against the Indemnitee), whether civil, criminal, administrative or investigative, in which the Indemnitee may be involved, or threatened to be involved, as a party or otherwise, arising out of or incidental to the business or activities of or relating to the LLC (a “Claim”), regardless of whether such Indemnitee continues to be a Member or a director, manager, officer, employee, shareholder, controlling person, agent or representative of the LLC or the Member at the time any such liability or expense is paid or incurred, if such Indemnitee determined in good faith that such conduct was in the best interest of the LLC and such Indemnitee’s conduct did not constitute fraud, gross negligence or willful misconduct and was within the scope of the Indemnitee’s authority; provided that all claims for indemnification by an Indemnitee shall be made only against and shall be limited to the assets of the LLC and no Indemnitee shall have recourse against the Member with respect to any such Claim. The termination of any action, suit or proceeding by judgment, order, settlement or conviction, or upon a plea of nolo contendre or its equivalent shall not, in and of itself, create a presumption or otherwise constitute evidence that the Indemnitee’s conduct did constitute fraud, gross negligence or willful misconduct.

7.2. Expenses

Expenses incurred by an Indemnitee in defending any Claim subject to this Section 7 shall, from time to time, upon request by the Indemnitee, be advanced by the LLC prior to the fmal disposition of such Claim upon receipt by the LLC of an undertaking by or on behalf of the Indemnitee to repay such amount, together with interest on any such advance or advances at the rate equal to the lesser of (i) two percentage points above the “Federal short-term rate” as defined in the Internal Revenue Code section 1274(d)(1)(C)(i) and (ii) the maximum rate permitted under applicable law, promptly upon (and in no event more than ten days after) a determination in a judicial proceeding or a binding arbitration that such Indemnitee is not entitled to be indemnified as authorized in this Section 7.

7.3. Other Rights

The indemnification provided by this Section 7 shall be in addition to any other rights to which an Indemnitee may be entitled under any agreement or as approved by the Member, as a matter of law or equity, or otherwise, both as to an action in such Indemnitee’s capacity as the Member or as a director, manager, officer, employee, shareholder, controlling person, agent or representative of the LLC or the Member, and as to an action in another capacity, and shall

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continue as to an Indemnitee who has ceased to serve in such capacity with respect to those periods during which such Indemnitee served, and shall inure to the benefit of the heirs, successors, assigns and administrators of the Indemnitee. The provisions of this Section 7 shall be deemed to be a contract between the LLC and the Member and between the LLC and each director, manager, officer, employee, shareholder, controlling person, agent or representative of the LLC or of the Member who serves in such capacity at any time while this Section 7 and the relevant provisions of the laws of the State of Delaware and other applicable law, if any, are in effect, and any repeal or modification hereof shall not affect any rights or obligations then existing with respect to any state of facts or any Claim then or theretofore existing, or any Claim thereafter brought or threatened based in whole or in part on any such state of facts.

7.4. Notice

Promptly after receipt of notice of the commencement of any Claim, an Indemnitee will, if indemnification in respect thereof is to be sought against the LLC under this Section 7, notify the LLC of the initiation thereof, but the omission so to notify the LLC will not relieve the LLC from any liability that the LLC may have to such Indemnitee otherwise than under this Section 7, or under this Section 7, except to the extent that the LLC is adversely affected by such lack of notice.

7.5. Counsel

The LLC shall have the right to undertake, by counsel or other representatives of its own choosing, the defense or other resolution of any Claim. In the event that the LLC shall elect not to undertake such defense or other resolution within a reasonable time after notice of such Claim from an Indemnitee, or the LLC shall fail to defend or otherwise resolve such Claim, such Indemnitee (upon further written notice to the LLC) shall have the right to undertake the defense, compromise or settlement of such Claim, by counsel or other representatives of its own choosing, on behalf of and for the account and risk of the LLC.

7.6. Other Persons

Except as specifically provided in Section 7.3, the provisions of this Section 7 are for the benefit of the Indemnitees only, and shall not be deemed to create any rights for the benefit of any other person or entity.

7.7. Survival

The indemnification provided by this Section 7 shall survive any termination of this Agreement.

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8. DISSOLUTION AND LIQUIDATION

8.1. Effect of Dissolution

Upon dissolution, the LLC shall cease carrying on its business but shall not terminate until the winding up of the affairs of the LLC is completed, the assets of the LLC have been distributed as provided below and a Certificate of Cancellation of the LLC under the Act has been filed with the Secretary of State of the State of Delaware.

8.2. Liquidation Upon Dissolution

Upon the dissolution of the LLC, sole and plenary authority to effectuate the liquidation of the assets of the LLC shall be vested in the Member, which shall have full power and authority to sell, assign and encumber any and all of the LLC’s assets and to wind up and liquidate the affairs of the LLC in an orderly and business-like manner. The proceeds of liquidation of the assets of the LLC distributable upon a dissolution and winding up of the LLC shall be applied in the following order of priority:

(i) first, to the creditors of the LLC, which may include the Member as a creditor, in the order of priority provided by law, in satisfaction of all liabilities and obligations of the LLC (or any nature whatsoever, including, without limitation, fixed or contingent, matured or unmatured, legal or equitable, secured or unsecured), whether by payment or the making of reasonable provisions for payment thereof; and

(ii) thereafter, one hundred percent (100%) to the Member.

8.3. Winding Up and Certificate of Cancellation

The winding up of the LLC shall be completed when all of its debts, liabilities and obligations have been paid and discharged or reasonably adequate provisions therefore has been made, and all of the remaining property and assets of the LLC have been distributed to the Member. Upon the completion of the winding up of the LLC, a Certificate of Cancellation of the LLC shall be filed with the Delaware Secretary of State.

9. ASSIGNMENT OF MEMBERSHIP INTEREST

The Member may assign in whole or in part its membership interest in the LLC. If the Member assigns all of its membership interest in the LLC, the transferee shall be automatically be admitted as a member of the LLC and immediately following such admission the transferor member shall cease to be a member of the LLC.

10. AMENDMENT

This Agreement may be amended or modified by a written instrument executed by the Member.

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11. GOVERNING LAW

This Agreement shall be governed and construed in accordance with the laws of the State of Delaware without regard to any applicable conflicts of law.

IN WITNESS WHEREOF, the undersigned has duly executed this Agreement, as of the day and year first herein above set forth.

Peabody Colorado Operations, LLC

By: /s/ ▇▇▇▇▇▇▇ ▇. ▇▇▇▇▇▇

Name: ▇▇▇▇▇▇▇ ▇. ▇▇▇▇▇▇

Its: Vice President and Secretary

Being the Sole Member of

Hayden Gulch Terminal, LLC

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