June 29, 2020 Dear Stockholder:

Exhibit (a)(1)(H)

June 29, 2020

Dear Stockholder:

I am pleased to inform you that, on June 24, 2020, Tetraphase Pharmaceuticals, Inc. (“Tetraphase”) entered into an Agreement and Plan of Merger (the “Merger Agreement”) with La Jolla Pharmaceutical Company (“Parent”) and TTP Merger Sub, Inc. (“Purchaser”), a wholly owned subsidiary of Parent. In accordance with the Merger Agreement, on June 29, 2020, Purchaser commenced a tender offer (the “Offer”) to acquire all of the outstanding shares of common stock of Tetraphase (the “Shares”) at a price per Share of $2.00 to the holder in cash, without interest, and less any applicable withholding taxes (the “Cash Amount”), plus one non-transferable contractual contingent value right per Share (each, a “CVR”), which CVR represents the right to receive one or more payments in cash, currently estimated to be up to approximately $1.48 per CVR, assuming the anticipated maximum number of CVRs are issued and contingent upon the achievement of certain milestones (the Cash Amount plus one CVR, collectively the “Offer Price”).

If successful, the Offer will be followed by the merger of Purchaser with and into Tetraphase, with Tetraphase surviving the merger as a wholly owned subsidiary of Parent (the “Merger”). The date and time at which the Merger becomes effective is referred to as the “Effective Time.” In the Merger, all then outstanding Shares (other than (i) Shares held by Tetraphase (or held in the treasury of Tetraphase), (ii) Shares held by La Jolla, Purchaser or any other direct or indirect wholly owned subsidiary of La Jolla, and (iii) Shares held by stockholders who have properly exercised and perfected their demands for appraisal of such Shares in accordance with the Delaware General Corporation Law (“DGCL”) and have neither withdrawn nor lost such rights prior to the Effective Time) will be converted into the right to receive consideration equal to the Offer Price, without interest, and subject to any applicable withholding of taxes.

The Board of Directors of Tetraphase (the “Board”) unanimously: (i) determined that the Merger Agreement and the transactions contemplated thereby, including the Offer and the Merger (the “Transactions”), are fair to, and in the best interest of, Tetraphase and its stockholders, (ii) declared it advisable for Tetraphase to enter into the Merger Agreement, (iii) approved the execution, delivery and performance by Tetraphase of the Merger Agreement and the consummation of the Transactions, (iv) resolved that the Merger shall be effected under Section 251(h) of the DGCL and (v) resolved to recommend that the stockholders of Tetraphase accept the Offer and tender their Shares to Purchaser pursuant to the Offer. The Boards of Directors of Parent and Purchaser have each approved the Merger Agreement and the transactions contemplated thereby.

Accompanying this letter is a copy of Tetraphase’s Solicitation/Recommendation Statement on Schedule 14D-9. Also enclosed are Purchaser’s offer to purchase, dated June 29, 2020, and a letter of transmittal for use in tendering your Shares and other related documents. These documents set forth the terms and conditions of the Offer. We urge you to read the enclosed materials carefully. The Offer is scheduled to expire at one minute after 11:59 P.M., Eastern time, on July 27, 2020, unless extended or terminated.

Very Truly Yours,

/s/ Xxxxx Xxxxxxx

Xxxxx Xxxxxxx

President and Chief Executive Officer