AMENDMENT NO.2 TO THIRD AMENDED AND RESTATED INVESTOR RIGHTS AGREEMENT

Exhibit 4.2(c)

Amendment No. 2 to

Third Amended and Restated Investor Rights Agreement

THIS AMENDMENT NO. 2 to the Third Amended and Restated Investor Rights Agreement dated March 16, 2006 (this “Amendment”) amends the Third Amended and Restated Investor Rights Agreement dated May 12, 2004, as amended (the “Future IRA”) by and among Targacept, Inc. (the “Company”) and the holders of shares of the Company’s Series C Convertible Preferred Stock, $0.001 par value per share (“Series C Stock”), Series B Convertible Preferred Stock, $0.001 par value per share (“Series B Stock”), or Series A Convertible Preferred Stock, $0.001 par value per share (“Series A Stock” and, together with the Series C Stock and Series B Stock, “Preferred Stock”) party thereto. Capitalized terms used herein and not otherwise defined shall have the meanings ascribed to them in the Future IRA.

R E C I T A L S:

WHEREAS, the Future IRA was entered into in contemplation of an initial public offering of the Company’s common stock in order to amend, effective as of the closing of such initial public offering, the Company’s Second Amended and Restated Investor Rights Agreement dated November 26, 2002, as amended (the “Current IRA”), which is currently in effect; and

WHEREAS, by its terms, the Future IRA would not become effective or affect the Current IRA unless and until the prospective initial public offering is completed and would not become effective at all if such initial public offering was not completed on or before June 30, 2005 (the “Trigger Date”); and

WHEREAS, Section 3 of the Future IRA provides that the Future IRA may be amended only with the prior written consent of the Company and the holders of a majority of the outstanding Series A Registrable Securities and Series B Registrable Securities and at least 65% of the outstanding Series C Registrable Securities (collectively, the “Required Investors”); and

WHEREAS, the prospective initial public offering was not completed on or before the Trigger Date, and the Company and the undersigned holders of Preferred Stock, constituting the Required Investors, desire to amend the Future IRA as provided herein to provide for a later Trigger Date;

NOW, THEREFORE, the undersigned parties agree as follows:

1. Section 9 of the Future IRA is hereby amended by replacing “June 30, 2005” therein with “September 30, 2006.”

2. As expressly amended hereby, the Future IRA shall continue in full force and effect.

[signature page follows]

IN WITNESS WHEREOF, this Amendment No. 2 to the Third Amended and Restated IRA is executed as of the day and year first above written.

TARGACEPT, INC.

By: /s/ J. Donald deBethizy

        Name: J. Donald deBethizy

        Title: President and CEO

R.J. REYNOLDS TOBACCO HOLDINGS, INC.

By: /s/ Charles A. Blixt

        Name: Charles A. Blixt

        Title: President

EUCLIDSR PARTNERS, L.P.

By: EuclidSr Associates, L.P.,

        its general partner

        By:/s/ Elaine V. Jones

                Elaine V. Jones

                General Partner

EUCLIDSR BIOTECHNOLOGY PARTNERS, L.P.

By: EuclidSr Biotechnology Associates, L.P.,

        its general partner

        By: /s/ Elaine V. Jones

                Elaine V. Jones

                General Partner

BURRILL BIOTECHNOLOGY CAPITAL FUND, L.P.

By: Burrill & Company (Biotechnology GP), LLC,

        its General Manager

        By: /s/ GS Burrill

                G. Steven Burrill

                Managing Member

[signatures continue on following page]

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GENAVENT FUND

By: SGAM Alternative Investments, its Manager

        By: /s/ Jean-Yves Nothias

                Jean-Yves Nothias

                Managing Director