Exhibit (a)(4)

Letter to Brokers and Dealers with respect to

Offer to Purchase for Cash

All Outstanding Shares of Common Stock

(including the Associated Rights to Purchase Series A Junior Participating Preferred Stock)

of

CV Therapeutics, Inc.

to

Apex Merger Sub, Inc.,

a wholly-owned subsidiary of

Gilead Sciences, Inc.

THE OFFER (AS DEFINED HEREIN) AND WITHDRAWAL RIGHTS WILL EXPIRE AT 12:00 MIDNIGHT (ONE MINUTE AFTER 11:59 P.M.), NEW YORK CITY TIME, ON APRIL 14, 2009, UNLESS THE OFFER IS EXTENDED. SHARES TENDERED PURSUANT TO THE OFFER MAY BE WITHDRAWN AT ANY TIME PRIOR TO THE EXPIRATION TIME OF THE OFFER.

March 18, 2009

To Brokers, Dealers, Banks,

Trust Companies and other Nominees:

We have been engaged by Apex Merger Sub, Inc., a Delaware corporation (“Acquisition Sub”) and a wholly-owned subsidiary of Gilead Sciences, Inc., a Delaware corporation (“Gilead”), to act as the information agent (the “Information Agent”) in connection with Acquisition Sub’s offer to purchase all of the outstanding shares of common stock, par value $0.001 per share (“Shares”), including all associated Rights (as defined below), of CV Therapeutics, Inc., a Delaware corporation (“CV Therapeutics”), at a price of $20.00 per share, net to the seller in cash, without interest thereon (the “Offer Price”), upon the terms and subject to the conditions set forth in Acquisition Sub’s Offer to Purchase, dated March 18, 2009 (the “Offer to Purchase”), and in the related Letter of Transmittal (which, together with any amendments or supplements thereto, collectively constitute the “Offer”). Please furnish copies of the enclosed materials to those of your clients for whom you hold Shares that are registered in your name or in the name of your nominee. All references to shares of CV Therapeutics common stock shall be deemed to include all associated rights (“Rights”) to purchase Series A Junior Participating Preferred Stock issued pursuant to the First Amended and Restated Rights Agreement, dated as of July 19, 2000, between CV Therapeutics and Wells Fargo Bank Minnesota, N.A., as amended from time to time.

Holders of Shares who wish to tender their Shares but whose certificates for such Shares (the “Share Certificates”) are not immediately available, who cannot complete the procedures for book-entry transfer on a timely basis, or who cannot deliver all other required documents to BNY Mellon Shareowner Services (the “Depositary”) prior to the Expiration Time (as defined in the Offer to Purchase) of the Offer must tender their Shares according to the guaranteed delivery procedure set forth in the Section 2 of Offer to Purchase.

Enclosed herewith are copies of the following documents:

1. The Offer to Purchase dated March 18, 2009;

2. The Letter of Transmittal to be used by stockholders of CV Therapeutics to tender Shares in the Offer (manually signed photocopies of the Letter of Transmittal may also be used to tender Shares);

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3. A letter to stockholders of CV Therapeutics from the Chairman and Chief Executive Officer of CV Therapeutics accompanied by CV Therapeutics’ Solicitation/Recommendation Statement on Schedule 14D-9 filed with the Securities and Exchange Commission by CV Therapeutics, which includes the recommendation of CV Therapeutics’ board of directors that CV Therapeutics stockholders accept the Offer and tender their Shares to Acquisition Sub pursuant to the Offer;

4. A printed form of letter that may be sent to your clients for whose account you hold Shares that are registered in your name or in the name of your nominee, with space provided for obtaining such clients’ instructions with regard to the Offer;

5. Notice of Guaranteed Delivery to be used to accept the Offer if Share Certificates are not immediately available or if such certificates and all other required documents cannot be delivered to the Depositary or if the procedures for book-entry transfer cannot be completed on a timely basis;

6. Instructions for Certification of Taxpayer Identification Number on Substitute Form W-9; and

7. Return envelope addressed to BNY Mellon Shareowner Services as the Depositary for the Offer.

We urge you to contact your clients promptly. Please note that the Offer and withdrawal rights will expire at 12:00 midnight (one minute after 11:59 p.m.), New York City time, on April 14, 2009, unless the Offer is extended.

The Offer is conditioned upon, among other things, there being validly tendered in accordance with the terms of the Offer and not withdrawn prior to the Expiration Time of the Offer, that number of Shares that, together with any shares of CV Therapeutics common stock then owned by Gilead or Acquisition Sub, represent more than 50% of the “Adjusted Outstanding Share Number”, which is defined as the sum of the aggregate number of shares of CV Therapeutics common stock issued and outstanding immediately prior to the acceptance for payment of shares pursuant to the Offer (the “Acceptance Time”), plus, at the election of Gilead, an additional number of shares up to (but not exceeding) the sum of (A) the aggregate number of shares of CV Therapeutics common stock issuable upon the exercise of all outstanding options, warrants and other rights to acquire CV Therapeutics common stock that are outstanding immediately prior to the Acceptance Time and that are vested and exercisable or will be vested and exercisable prior to the completion of the Merger, plus (B) the aggregate number of shares of CV Therapeutics common stock issuable upon conversion of all of CV Therapeutics’ convertible debt securities that are outstanding immediately prior to the Acceptance Time and that are convertible into such shares or will be convertible into such shares prior to the completion of the Merger. The foregoing condition is referred to as the “Minimum Condition” in the Offer to Purchase. The Offer is subject to certain other conditions described in Sections 1 and 13 of the Offer to Purchase.

The Offer is being made pursuant to an Agreement and Plan of Merger, dated as of March 12, 2009 (the “Merger Agreement”), by and among Gilead, Acquisition Sub and CV Therapeutics pursuant to which following the satisfaction or waiver of certain conditions and the purchase of shares of CV Therapeutics common stock in the Offer, Acquisition Sub will be merged with and into CV Therapeutics (the “Merger”), with CV Therapeutics surviving the Merger as a wholly-owned subsidiary of Gilead. As a result of the Merger, each outstanding Share (other than Shares owned by Gilead, Acquisition Sub, CV Therapeutics or any wholly-owned subsidiary of Gilead, Acquisition Sub or CV Therapeutics, or by any stockholder of CV Therapeutics who is entitled to and properly preserves appraisal rights under Delaware law) will be converted into the right to receive the price per Share paid in the Offer in cash, without interest thereon.

The CV Therapeutics board of directors has unanimously: (1) determined that the Merger Agreement and the transactions contemplated thereby, including the Offer and the Merger, are fair to and in the best interests of CV Therapeutics’ stockholders; (2) approved the Merger Agreement and the transactions contemplated thereby, including the Offer and the Merger, in accordance with the requirements of the Delaware General Corporation Law; (3) declared that the Merger Agreement is advisable; and (4) resolved to recommend that CV Therapeutics’

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stockholders accept the Offer and tender their shares of CV Therapeutics common stock pursuant to the Offer and, if required, adopt the Merger Agreement.

On the terms of and subject to the conditions to the Offer (including, if the Offer is extended or amended, the terms and conditions of any such extension or amendment), promptly after the Expiration Time of the Offer, Acquisition Sub will accept for payment, and pay for, all Shares validly tendered to Acquisition Sub and not withdrawn prior to the Expiration Time of the Offer. To validly tender Shares in the Offer (i) the certificate(s) representing the tendered Shares, together with the Letter of Transmittal (or a photocopy of the Letter of Transmittal), properly completed and duly executed, together with any required signature guarantees, and any other required documents, must be received by the Depositary prior to the Expiration Time of the Offer, (ii) in the case of a tender effected pursuant to the book-entry transfer procedures described in the Offer to Purchase (a) either the Letter of Transmittal, properly completed and duly executed, together with any required signature guarantees, or an Agent’s Message (as defined in the Offer to Purchase) and any other required documents, must be received by the Depositary prior to the Expiration Time of the Offer, and (b) the Shares to be tendered must be delivered pursuant to the book-entry transfer procedures described in the Offer to Purchase and a Book-Entry Confirmation (as defined in the Offer to Purchase), must be received by the Depositary prior to the Expiration Time of the Offer or (iii) the tendering stockholder must comply with the guaranteed delivery procedures described in the Offer to Purchase prior to the Expiration Time of the Offer.

Neither Acquisition Sub nor Gilead will pay any fees or commissions to any broker or dealer or other person (other than the Depositary and the Information Agent) in connection with the solicitation of tenders of Shares in connection with the Offer. You will be reimbursed by Acquisition Sub upon request for customary mailing and handling expenses incurred by you in forwarding the enclosed materials to your customers. Acquisition Sub will pay or cause to be paid all stock transfer taxes applicable to its purchase of Shares pursuant to the Offer, except as otherwise provided in Instruction 6 of the Letter of Transmittal.

Questions regarding the Offer, and requests for additional copies of the enclosed material, may be directed to the Information Agent at its address and telephone number listed on the back cover of the Offer to Purchase.

Very truly yours,

INNISFREE M&A INCORPORATED

NOTHING CONTAINED HEREIN OR IN THE ENCLOSED DOCUMENTS SHALL RENDER YOU OR ANY OTHER PERSON THE AGENT OF ACQUISITION SUB, GILEAD, THE DEPOSITARY OR THE INFORMATION AGENT OR AUTHORIZE YOU OR ANY OTHER PERSON TO GIVE ANY INFORMATION OR MAKE ANY REPRESENTATION ON BEHALF OF ANY OF THEM WITH RESPECT TO THE OFFER NOT CONTAINED IN THE OFFER TO PURCHASE OR THE LETTER OF TRANSMITTAL FOR THE OFFER.

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