Exhibit 10.9

CONSULTING AGREEMENT

This Consulting Agreement (this “Agreement”) is entered into as of September 1, 2008, between CoLucid Pharmaceuticals, Inc., a corporation organized under the laws of Delaware (the “Company”), and LLH Associates, LLC, a limited liability company organized under the laws of New Jersey (the “Consulting Firm”). The Company wishes to retain the Consulting Firm as an independent contractor to perform consulting services for the Company, and the Consulting Firm is willing to perform such services, on the terms set forth herein. The parties hereto have entered into a Confidentiality Agreement, dated as of July 16, 2008 (the “Confidentiality Agreement”), in contemplation of the services referred to herein.

Therefore, in consideration of the mutual promises set forth herein, the parties agree as follows:

1. Consulting Services. The Consulting Firm shall cause the following services (the “Consulting Services”) to be performed for the Company exclusively by Linda C. Hogan (the “Consultant”):

(a) The Consultant shall not be an officer of the Company but shall have the title “Vice President, Business Development.”

(b) The Consultant shall provide strategic advice to the Company with respect to its business plan, business development strategies and other matters, as requested from time to time by the Board of Directors of the Company (the “Board”) and/or Chief Executive Officer.

(c) Subject to the direction and authority of the Board and the Chief Executive Officer, the Consultant shall assist the Chief Executive Officer in directing the Company’s efforts and activities with respect to merger and acquisition transactions involving any or all of the Company’s assets or the Company as a whole and with respect to partnering, strategic alliance, collaboration, licensing, co-development and similar transactions involving any of the Company’s assets, compounds or programs.

The Consultant shall devote, on average, two days per week to the Consulting Services. The parties acknowledge that the term “Services” as used in the Confidentiality Agreement refers to the Consulting Services.

The Company shall indemnify and hold harmless the Consulting Firm and Consultant from any losses, expenses, claims or proceedings arising from (i) any inaccurate or incomplete information provided by the Company to the Consultant or to any third party in connection with the Consulting Services; (ii) any action or inaction by the Consultant in connection with the Consulting Services taken or not taken pursuant to the express direction of the Company; or (iii) any other matter in connection with the Consulting Services not involving negligence or more culpable conduct on the part of the Consultant. The foregoing indemnity shall (x) survive the termination or expiration of this Agreement, (y) be in addition to any rights the Consulting Firm or Consultant may have at common law or otherwise, and (z) inure to the benefit of any successors, assigns or personal representatives of the Consulting Firm and Consultant.

2. Compensation. In consideration for the Consulting Services and the covenants and agreements of the Consulting Firm and Consultant pursuant to this Agreement and the Confidentiality Agreement, the Company shall pay to the Consulting Firm a consulting fee in the amount of $10,000 for each full month (pro rated for partial months) during the term of this Agreement, and shall reimburse the Consulting Firm for its reasonable and properly documented out-of-pocket expenses in accordance with Company policies. If the Company consummates a sale or partnering transaction with respect to any of the compounds developed from its stigmine platform, the Company will consider payment to the Consulting Firm of a discretionary cash bonus in an amount to be determined by the Board, but the Company shall not be obligated to make any such payment. The Company shall grant to the Consulting Firm options (“Options”) to purchase shares of the Company’s common stock (“Shares”) as follows:

(a) No later than the first meeting of the Board that is held after October 1, 2008, the Company shall grant to the Consulting Firm Options to purchase 115,516 Shares, representing 0.33% of the number of Fully Diluted Shares as of the date hereof. For purposes hereof, the term “Fully Diluted Shares” means, as of any time, the total number of Shares (i) issued and outstanding as of such time, (ii) reserved for issuance pursuant to stock option or equity incentive plans in effect as of such time, and (iii) issuable upon conversion of any outstanding convertible securities or upon exercise of any outstanding warrants as of such time.

(b) If the Company closes, during the term of this Agreement, the second tranche of its Series B financing, then the Company shall evaluate a potential grant to the Consulting Firm of Options to purchase a number of Shares determined by the Board and, for purposes of such evaluation, the Board shall apply a methodology consistent with the methodology applied to Vice Presidents of the Company, but the Company shall not be obligated to make any such grant.

(c) If the Company consummates, during the term of this Agreement, a Major Transaction approved by the Board (and the stockholders, if required), then the Company shall grant to the Consulting Firm Options to purchase a number of Shares such that the Consulting Firm’s Equity Holdings upon issuance of such Option constitute 1% of the number of Fully Diluted Shares at that time. For purposes hereof:

(i) the term “Major Transaction” means either (x) a transaction as a result of which a third party (excluding existing preferred stockholders and other parties who in the future provide venture capital or other financing to the Company) acquires majority voting control of the Company or acquires all or substantially all of the Company’s assets and rights related to its migraine compound (COL-144) and related development program, or (y) a collaboration, strategic alliance or other partnering transaction pursuant to which the Company grants to a third party exclusive rights to develop and commercialize the Company’s migraine compound (COL-144); and

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(ii) the term “Consulting Firm’s Equity Holdings” means, as of any time, the sum of (x) the number of Shares then owned by the Consulting Firm, plus (y) the number of Shares then subject to Options, whether or not vested, held by the Consulting Firm; provided that if any Shares or Options have been transferred or disposed of by the Consulting Firm to the Consultant or otherwise, then those Shares or Options shall be treated as if they were still owned or held by the Consulting Firm.

(d) Each of the Options:

(i) shall be granted only if the Board determines, in its reasonable discretion, that the Consulting Firm and Consultant have, from the date hereof through the date of grant, performed the Consulting Services in a satisfactory manner and complied with their obligations pursuant to this Agreement and the Confidentiality Agreement;

(ii) shall be governed by and subject to the Company’s 2006 Equity Incentive Plan and an option agreement in form and substance acceptable to the Company;

(iii) shall be “nonqualified” under applicable tax laws;

(iv) shall have an exercise price per share equal to the fair market value of one Share as of the date of grant, as determined by the Board; and

(v) shall vest as to 25% of the Shares on September 24, 2009, and as to the remaining 75% of the Shares in equal monthly installments on the last day of each month, beginning October 31, 2009, over the following 36 months.

3. Efforts and Devotion to Duties. The Consulting Firm shall devote its best efforts (and shall cause the Consultant to devote her best efforts) to fulfilling its obligations hereunder and to do nothing that would harm the business or reputation of the Company. During the term of this Agreement, the Consulting Firm and Consultant shall be free to engage in other business activities that do not adversely affect the Consulting Services, so long as such other activities are not in competition with the Company and are not inconsistent with this Agreement. The Consulting Firm and Consultant represent and warrant to the Company that they have no existing obligation or commitment that conflicts with this Agreement or that would preclude them from performing their responsibilities hereunder, and they agree not to enter into any such conflicting obligation or commitment.

4. Relationship and Authority. The Consulting Firm and Consultant shall be independent contractors (not employees) with respect to the Company and shall have no authority to bind the Company or make commitments on its behalf. Except as stated in the

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preceding sentence, this Agreement shall not be deemed to create any employment, partnership, agency or other relationship between the Company, on the one hand, and the Consulting Firm or Consultant, on the other hand. The Consulting Firm and Consultant shall have no right to participate in any employee benefit plan or arrangement of the Company. If the Consulting Firm and/or Consultant are reclassified by any governmental authority as employees of the Company, they shall have no right to any Company benefits, except as required by law, even if they would be eligible therefor by the terms of the applicable benefit plans or arrangements.

5. Term and Termination. The term of this Agreement shall continue indefinitely until such time as this Agreement is terminated by either the Company or the Consulting Firm upon at least 10 days’ prior written notice to the other. Upon termination of this Agreement, the Company’s sole obligation to the Consulting Firm and Consultant shall be to pay any compensation earned through the termination date pursuant to Section 2 above. Immediately following termination, the Consulting Firm and Consultant shall deliver to the Company all Company property in the possession or under the control of the Consulting Firm or Consultant. All work product received, developed or created by the Consulting Firm and/or Consultant, alone or with others, during the performance of the Consulting Services (including, without limitation, all records, documents, notes, data and other materials of any nature pertaining to the Consulting Services or reflecting confidential or proprietary information, trade secrets or other intellectual property of the Company) shall be deemed to be Company property; provided that the materials described in Appendix A to the Confidentiality Agreement shall be deemed to be property of the Consulting Firm.

6. Miscellaneous.

(a) No Assignment or Subcontracting without Consent. No party hereto may assign any of its rights or obligations under this Agreement without the written consent of the other, except that the Company shall have the right to assign any or all of its rights or obligations hereunder to any of its affiliates or to any successor company that acquires substantially all of the business operations to which the Consulting Services relate. Without limiting the generality of the foregoing, the Consulting Firm and Consultant shall not subcontract or delegate any of the services hereunder without the prior written consent of the Company.

(b) Entire Agreement. This Agreement and the Confidentiality Agreement together constitute the entire agreement, and supersede all prior agreements and understandings, written and oral, between the parties with respect to the Consulting Services.

(c) Waivers. The failure by any party at any time to require performance of any provision hereof shall not affect its right later to require such performance. No waiver in any one or more instances shall (except as otherwise stated therein) be deemed to be a further or continuing waiver of any such condition or breach in any other instances or a waiver of any other condition or breach of any other term, covenant, representation or warranty.

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(d) Counterparts. This Agreement may be executed in one or more counterparts, each of which shall be deemed to be an original but all of which together shall constitute one and the same instrument.

(e) Governing Law. This Agreement shall be governed by and construed and enforced exclusively in accordance with the laws of the State of Indiana, without regard to the conflicts of law principles thereof.

(f) Notices. All notices and other communications in connection with this Agreement shall be in writing and shall be sent to the respective parties at the following addresses (or such other addresses as they may designate in accordance herewith) by registered or certified mail, postage prepaid, or by express courier service, service fee prepaid, or by facsimile with a hard copy to follow via mail or express courier service in accordance with this paragraph.

All notices shall be deemed given and received (i) if delivered by hand, immediately, (ii) if sent by mail, three business days after posting, (iii) if delivered by express courier service, the next business day, or (iv) if sent by facsimile, at the time shown in the confirmed electronic receipt or on the first business day thereafter if the notice is sent on a day other than a business day.

(g) Amendments. This Agreement may be amended only by an instrument in writing executed by the parties sought to be bound thereby.

(h) Injunctive Relief. The Consulting Firm and Consultant acknowledge that any violation or threatened violation of this Agreement will cause irreparable harm to the Company that is incapable of precise measurement and that, as a result, the Company will not have an adequate remedy at law to redress such harm. Therefore, in addition to monetary damages and other remedies, the Company shall be entitled to injunctive relief, including temporary restraining orders and/or preliminary or permanent injunctions, without posting bond.

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As evidence of their acceptance of the terms set forth herein, the Company and the Consulting Firm have executed this Agreement as of the date stated in the opening paragraph.

By signing below, the Consultant joins into this Agreement for the purpose of acknowledging her obligations and responsibilities hereunder.

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