HALLIBURTON COMPANY And JPMORGAN CHASE BANK, NATIONAL ASSOCIATION (formerly JPMorgan Chase Bank), as Trustee FIRST SUPPLEMENTAL INDENTURE Dated as of December 17, 2004 31/8% Convertible Senior Notes due July 15, 2023 HALLIBURTON COMPANY FIRST...

EXHIBIT 4.1

HALLIBURTON COMPANY

And

JPMORGAN CHASE BANK, NATIONAL ASSOCIATION

(formerly JPMorgan Chase Bank),

as Trustee

__________________

FIRST SUPPLEMENTAL INDENTURE

Dated as of December 17, 2004

_________________

3¹/₈% Convertible Senior Notes due July 15, 2023

HALLIBURTON COMPANY

FIRST SUPPLEMENTAL INDENTURE

3¹/₈% Convertible Senior Notes due July 15, 2023

FIRST SUPPLEMENTAL INDENTURE, dated as of December 17, 2004, between HALLIBURTON COMPANY, a Delaware corporation (the “Company”), and JPMORGAN CHASE BANK, NATIONAL ASSOCIATION (formerly JPMorgan Chase Bank), as Trustee (the “Trustee”).

RECITALS

The Company has heretofore executed and delivered to the Trustee an Indenture, dated as of June 30, 2003 (the “Indenture”), providing for the issuance of the Company’s “3¹/₈% Convertible Senior Notes due July 15, 2023” (the “Notes”).

Sections 9.2 and 9.17 of the Indenture permit the Company, at its option, to settle conversions of the Notes in common stock of the Company, in cash or in a combination of cash and stock. Pursuant to the terms of the Indenture, the Company seeks to amend the Indenture to limit the Company’s right to settle any conversion of the Notes through delivery of shares of common stock of the Company.

Subparagraph (6) of Section 13.1 of the Indenture provides that the Company and the Trustee may amend the Indenture or the Notes, without notice to or consent of any Holder, in any manner necessary or desirable that will not adversely affect the rights of any Holder.

The Company and the Trustee agree as follows:

ARTICLE I

Relation to Indenture

Section 101 Relation to Indenture. This First Supplemental Indenture amends the Indenture as provided in ARTICLE II below and constitutes an integral part of the Indenture.

ARTICLE II

Amendment of First Supplemental Indenture

Section 201 Amendment of Section 9.2. Section 9.2 of the Indenture is hereby amended and restated to read as follows:

“SECTION 9.2 Conversion Procedures. To convert Notes, a Holder must satisfy the requirements in this Section 9.2 and in paragraph 9 of the Notes. The date on which the Holder satisfies all those requirements and delivers an irrevocable conversion notice, together, if the Notes are in certificated form, with the certificated Note, to the Conversion Agent along with appropriate endorsements and transfer documents, if required, and pays any transfer or similar tax, if required, is the conversion date (the “Conversion Date”). As soon as practicable, but in no event later than the fifth Business Day following the Conversion Date, the Company shall deliver to the Holder, through the Conversion Agent, cash or a combination of cash and shares of Common Stock as set forth in Section 9.17 and cash in lieu of any fractional share determined pursuant to Section 9.3. The Person in whose name any certificated Note is registered shall be treated as a stockholder of record on and after the Conversion Date; provided, however, that no surrender of Notes on any date when the stock transfer books of the Company shall be closed shall be effective to constitute the Person or Persons entitled to receive the shares of Common Stock upon such conversion as the record holder or holders of such shares of Common Stock on such date, but such surrender shall be effective to constitute the Person or Persons entitled to receive such shares of Common Stock as the record holder or holders thereof for all purposes at the close of business on the next succeeding day on which such stock transfer books are open; such conversion shall be at the Conversion Rate in effect on the date that such Notes shall have been surrendered for conversion, as if the stock transfer books of the Company had not been closed. Upon conversion of Notes, such Person shall no longer be a Holder of such Notes.

No payment or adjustment shall be made for dividends on or other distributions with respect to any Common Stock except as provided in Section 9.6 or as otherwise provided in this Indenture.

On conversion of Notes, that portion of accrued interest, if any, with respect to the converted Notes shall not be canceled, extinguished or forfeited, but rather shall be deemed to be paid in full to the Holder thereof through delivery of the cash or a combination of cash and Common Stock in exchange for the Notes being converted pursuant to the provisions hereof, and the cash shall be treated as issued, to the extent thereof, first in exchange for the principal amount of the Notes being converted pursuant to the provisions hereof and the balance, if any, of such cash or the Fair Market Value of such shares of Common Stock shall be treated as issued in exchange for interest accrued and unpaid through the Conversion Date. Notwithstanding conversion of any Notes, the Holders of the Notes and any Common Stock issuable upon conversion thereof will continue to be entitled to receive Additional Amounts in accordance with the Registration Rights Agreement.

If a Holder converts more than one Note at the same time, the cash or the combination of cash and shares of Common Stock issuable upon the conversion shall be based on the total principal amount of the Notes converted.

Upon surrender of a Note that is converted in part, the Company shall execute, and the Trustee or the Authenticating Agent shall authenticate and deliver to the Holder, a new Note in an authorized denomination equal in principal amount to the unconverted portion of the Note surrendered.

If the last day on which Notes may be converted is not a Business Day in a place where a Conversion Agent is located, the Notes may be surrendered to that Conversion Agent on the next succeeding Business Day.

Notes in respect of which a Holder has delivered a notice of exercise of the option to require the Company to purchase such Notes pursuant to Article VI or VII may be converted only if the notice of exercise is withdrawn in accordance with the terms of Section 8.2.”

Section 202 Amendment of Section 9.17. Section 9.17 of the Indenture is hereby amended and restated to read as follows:

“Section 9.17 Payment in Cash in Lieu of Common Stock. If a Holder elects to convert all or any portion of a Note as set forth in Section 9.1 and delivers an irrevocable conversion notice, together, if the Notes are in certificated form, with the certificated Note as set forth in Section 9.2, the Company may choose to satisfy all or any portion of its conversion obligation (the “Conversion Obligation”) in cash or a combination of cash and stock computed as follows:

(a)  if the Company elects to satisfy the entire Conversion Obligation in cash (“Cash Settlement”), the Company will deliver to such Holder cash in an amount equal to the product of: (1) a number equal to (x) the aggregate original principal amount at maturity of Securities to be converted divided by 1,000, multiplied by (y) the Conversion Rate, and (2) the average Closing Price of the Common Stock during the Cash Settlement Averaging Period (as defined below); and

(b)  if the Company elects to satisfy a fixed portion (other than 100%) of the Conversion Obligation in cash (the “Partial Cash Amount”), the Company will deliver to such Holder such Partial Cash Amount and a number of shares equal to the greater of (1) one and (2) the excess, if any, of (A) the number of shares equal to (i) the aggregate original principal amount at maturity of Securities to be converted divided by 1,000, multiplied by (ii) the Conversion Rate, over (B) the number of shares equal to the sum, for each day of the Cash Settlement Averaging Period, of (x) 10% of the Partial Cash Amount, divided by (y) the closing price of the Common Stock on such day. Cash will be paid in lieu of any fractional shares as provided by Section 9.3. In no event shall the Partial Cash Amount be less than the aggregate principal amount of the Notes to be converted.

Upon such election, the Company will notify such Holder through the Trustee of the dollar amount to be satisfied in cash (which must be expressed either as 100% of the Conversion Obligation or as a fixed dollar amount) at any time on or before the date that is three Business Days following receipt of written notice of conversion as specified in Section 9.2 (such period, the “Cash Settlement Notice Period”). The Holder may retract the conversion notice at any time during the two Business Day period beginning on the day after the final day of the Cash Settlement Notice Period (a “Conversion Retraction Period”). If the conversion notice has not been retracted, then settlement (in cash and/or shares) will occur on the Business Day following the final day of the 10 Trading Day period beginning on the day after the final day of the Conversion Retraction Period (the “Cash Settlement Averaging Period”).”

Section 203 Notes Deemed Conformed. As of the date hereof, the provisions of the Notes shall be deemed to be conformed, without the necessity for any reissuance or exchange of such Note or any other action on the part of the Holders of Notes, the Company or the Trustee, so as to reflect this First Supplemental Indenture.

ARTICLE III

Miscellaneous Provisions

Section 301 The Indenture, as supplemented and amended by this First Supplemental Indenture, is in all respects hereby adopted, ratified and confirmed.

Section 302 This First Supplemental Indenture may be executed in any number of counterparts, each of which shall be an original, but such counterparts shall together constitute but one and the same instrument.

Section 303 This First Supplemental Indenture shall be governed by and construed in accordance with the laws of the State of New York.

Section 304 If any provision in this First Supplemental Indenture limits, qualifies or conflicts with another provision hereof which is required to be included herein by any provisions of the Trust Indenture Act, such required provision shall control.

Section 305 In case any provision in this First Supplemental Indenture or the Notes shall be invalid, illegal or unenforceable, the validity, legality and enforceability of the remaining provisions shall not in any way be affected or impaired thereby.

Section 306 The Trustee assumes no duties, responsibilities or liabilities by reason of this First Supplemental Indenture other than as set forth in the Indenture.

IN WITNESS WHEREOF, the parties hereto have caused this First Supplemental Indenture to be duly executed, as of the day and year first written above.

		HALLIBURTON COMPANY
	By:	/s/ C. Xxxxxxxxxxx Xxxx
		C. Xxxxxxxxxxx Xxxx
		Executive Vice President and
		Chief Financial Officer

		JPMORGAN CHASE BANK, NATIONAL
		ASSOCIATION, as Trustee
	By:	/s/ Xxxxx Xxxxx
		Xxxxx Xxxxx
		Vice President and Trust Officer