CONSULTING AGREEMENT

Exhibit 10.6

CONSULTING AGREEMENT

THIS CONSULTING AGREEMENT (the “Agreement”) is made and entered into this 1st day of July, 2009 (the “Effective Date”) by and between CombinatoRx, Incorporated, a Delaware corporation duly organized under law and having a usual place of business at 245 First Street, Cambridge, MA 02142 (hereinafter referred to as the “Company”) and Alexis Borisy.

WHEREAS, the Consultant previously provided services to the Company as its President and CEO pursuant to that First Amended Employment, Confidentiality and Non-Competition Agreement, dated as of July 1, 2004, as amended on December 12, 2008 (the “Employment Agreement”),

WHEREAS, the Company and the Consultant have agreed to terminate the Consultant’s employment relationship with the Company under the Employment Agreement, and the Company wishes to engage the Consultant to provide the services described herein and Consultant agrees to provide the services for the compensation and otherwise in accordance with the terms and conditions contained in this Agreement,

NOW THEREFORE, in consideration of the foregoing, and for other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, accepted and agreed to, the Company and the Consultant, intending to be legally bound, agree to the terms set forth below.

1. TERM. Commencing as of the Effective Date, and continuing until June 30, 2010 (the “Term”), unless earlier terminated pursuant to Section 5 hereof, the Consultant agrees that he will serve as a member of the Company’s Scientific Advisory Board and as a consultant to the Company. This Agreement may be renewed or extended for any period as may be agreed by the parties.

2. DUTIES AND SERVICES.

(a) Consultant’s duties and responsibilities shall be as described in Exhibit “A,” annexed hereto and made a part hereof (collectively, the “Duties” or “Services”).

(b) The Consultant represents and warrants to the Company that he is under no contractual or other restrictions or obligations which are inconsistent with the execution of this Agreement, or which will interfere with the performance of his Duties. Consultant represents and warrants that the execution and performance of this Agreement will not violate any policies or procedures of any other person or entity for which he performs Services concurrently with those performed herein. Consultant understands and agrees that he will not bring to the Company or use in the performance of Consultant’s duties at the Company any materials or documents rightfully belonging to any other party which are not generally available to the public. Consultant may bring such materials and documents to the Company provided Consultant has

obtained written authorization from such other party for their possession and use. Further, Consultant agrees that he will not enter into any agreement (either written or oral) which would put Consultant in conflict with this Agreement and/or require that he disclose Confidential Information.

(c) In performing the Services, Consultant shall comply, to the best of his knowledge, with all business conduct and regulatory and health and safety guidelines, policies and regulations established by the Company or any governmental authority with respect to the Company’s business.

(d) Consultant represents that he has not been disbarred and, to the best of his knowledge, is not under consideration for disbarment by the Food and Drug Administration from working in or providing services to any pharmaceutical or biotechnology company under the Generic Drug Enforcement Act of 1992.

3. CONSULTING FEE.

(a) Subject to the provisions hereof, the Company shall pay Consultant a consulting fee as described in Appendix A. The Consultant shall submit monthly, on the Company’s standard reporting form, a listing of his hours, the Duties performed and a summary of his activities. The Consulting Fee shall be paid within thirty (30) days of the Company’s receipt of the report and invoice.

(b) Consultant shall be entitled to prompt reimbursement for all pre-approved expenses incurred in the performance of his Duties, upon submission and approval of written statements and receipts in accordance with the then regular procedures of the Company. Pre-approval is required for expenses in excess of $500.00.

4. RELATIONSHIP OF THE PARTIES.

(a) The Consultant agrees that all Services will be rendered by him as an independent contractor and this Agreement is not to be interpreted as creating an employment relationship between the Consultant and the Company or any of its Affiliates. It is agreed that, as an independent contractor, the Consultant will not attempt to bind the Company or any of its Affiliates to any obligation or pledge its credit, unless expressly authorized in writing by the CEO or another expressly authorized representative of the Company. Affiliates means all natural persons and entities controlling, controlled by or under common control with the Company, where control may be by management authority, contract or equity interest.

(b) Because the Consultant is an independent contractor with respect to the Company, the consulting fees paid under this Agreement are not subject to withholding for Social Security, unemployment, Medicare, federal, state or local income or other taxes. All taxes and other legally required payments and any insurance required by law shall be the sole responsibility of the Consultant. The Consultant agrees to pay all taxes, including self-employment taxes due in respect of the Consulting Fee and to indemnify the Company in the event the Company is required to pay any such taxes on behalf of Consultant.

(c) As an independent contractor, neither the Consultant nor anyone claiming through the Consultant shall be eligible to participate in, or receive benefits under, any bonus or other compensation plan or any stock option plan, employee benefit plan or other employee plan, program or arrangement of the Company or any of its Affiliates.

(d) The Consultant agrees and acknowledges that the Company will not maintain general liability or other insurance covering him. The Consultant will be solely responsible for comprehensive general liability, automobile and other insurance and will assume all risk in connection with the adequacy of any and all such insurance which the Consultant elects to obtain.

5. EARLY TERMINATION OF THE TERM.

(a) This Agreement may be terminated without cause by either party upon not less than thirty (30) days’ prior written notice by either party to the other.

(b) Upon termination under Section 5(a), neither party shall have any further obligations under this Agreement, except for the obligations which by their terms survive this termination as noted in Section 17 hereof. Upon termination, and in any case upon the Company’s request, Consultant shall return immediately to the Company all Confidential Information and copies thereof.

6. CONTINUING OBLIGATIONS. The Consultant acknowledges that he has continuing obligations to the Company pursuant to the terms of Sections 7, 8, 9 and 10 of the Employment Agreement and pursuant to the terms of the letter agreement with the Company dated July 1, 2009. The Consultant acknowledges those continuing obligations and agrees to abide by them.

7. PROPRIETARY RIGHTS.

(a) Definitions. For the purposes of this Section 7, the terms set forth below shall have the following meanings:

(i) Concept and Ideas. Those concepts and ideas disclosed by the Company to Consultant or which are first developed by Consultant during the course of the performance of Services hereunder and which relate to the Company’s present, past or prospective business activities, services, and products, all of which shall remain the sole and exclusive property of the Company. The Consultant shall have no publication rights, and all of the same shall belong exclusively to the Company.

(ii) Confidential Information. For the purposes of this Agreement, Confidential Information shall mean and collectively include all information relating to the business, plans and/or technology of the Company including but not limited to technical information, including inventions, methods, plans, processes, specifications, characteristics, assays, raw data, scientific preclinical or clinical data, records, databases, formulations, clinical protocols, equipment design, know-how, experience, and trade secrets; developmental,

marketing, sales, customer, supplier, consulting relationship information, operating, performance, and cost information; computer programming techniques; microscopy technology and signal identification strategy whether in tangible or intangible form; and, all record bearing media containing or disclosing the foregoing information and techniques, including written business plans, patents and patent applications, grant applications, notes, and memoranda, whether in writing or presented, stored or maintained in or by electronic, magnetic, or other means.

Notwithstanding the foregoing, the term “Confidential Information” shall not include any information which: (a) can be demonstrated to have been in the public domain or was publicly known or available prior to the date of the disclosure to Consultant; (b) can be demonstrated in writing to have been rightfully in the possession of Consultant prior to the disclosure of such information to Consultant by the Company; (c) becomes part of the public domain or publicly known or available by publication or otherwise, not due to any unauthorized act or omission on the part of Consultant; or (d) is supplied to Consultant by a third party without binder of secrecy, provided, however, that such third party has no obligation to the Company or any of its Affiliates to maintain such information in confidence.

(b) Non-Disclosure to Third Parties. Except as required by Consultant’s Duties, Consultant shall not, at any time now or in the future, directly or indirectly, use, publish, disseminate or otherwise disclose any Confidential Information, Concepts, or Ideas to any third party without the prior written consent of the Company which consent may be denied in each instance and all of the same, together with publication rights, shall belong exclusively to the Company.

(c) Documents, etc. All documents, diskettes, tapes, procedural manuals, guides, specifications, plans, drawings, designs and similar materials, lists of present, past or prospective customers, customer proposals, invitations to submit proposals, price lists and data relating to the pricing of the Company’s products and services, records, notebooks and all other materials containing Confidential Information or information about Concepts or Ideas (including all copies and reproductions thereof) that come into Consultant’s possession or control by reason of Consultant’s performance of the relationship, whether prepared by Consultant or others: (a) are the property of the Company; (b) will not be used by Consultant in any way other than in connection with the performance of his Duties; (c) will not be provided or shown to any third party by Consultant; (d) will not be removed from the Company’s or Consultant’s premises (except as Consultant’s Duties require); and (e) at the termination (for whatever reason) of Consultant’s relationship with the Company, or at such earlier time as requested by the Company, will be left with, or forthwith returned by Consultant to the Company.

(d) Patents, etc. The Consultant agrees that the Company is and shall remain the exclusive owner of the Confidential Information and Concepts and Ideas. Any interest in patents, patent applications, inventions, technological innovations, trade names, trademarks, service marks, copyrights, copyrightable works, developments, discoveries, designs, processes, formulas, know-how, data and analysis, whether registrable or not (“Developments”), which Consultant, as a result of rendering Services to the Company under this Agreement, may conceive or develop, shall: (i) forthwith be brought to the attention of the Company by Consultant and (ii) belong exclusively to the Company. No license or conveyance of any such rights to the Consultant is granted or implied under this Agreement.

(e) Assignment. The Consultant hereby assigns and, to the extent any such assignment cannot be made at present, hereby agrees to assign to the Company, without further compensation, all of his right, title and interest in and to all Concepts, Ideas, and Developments. The Consultant will execute all documents and perform all lawful acts which the Company considers necessary or advisable to secure its rights hereunder and to carry out the intent of this Agreement. Consultant’s obligation to assist the Company in effecting such assignment(s), in any and all countries shall continue beyond the termination or expiration of this Agreement.

8. EQUITABLE RELIEF. Consultant agrees that any breach of Sections 6 and 7 above by him would cause irreparable damage to the Company and that, in the event of such breach, the Company shall have, in addition to any and all remedies of law, the right to an injunction, specific performance or other equitable relief to prevent the violation or threatened violation of Consultant’s obligations hereunder, without the requirement of having to post bond.

9. WAIVER. Any waiver by the Company of a breach of any provision of this Agreement shall not operate or be construed as a waiver of any subsequent breach of the same or any other provision hereof. All waivers by the Company shall be in writing.

10. SEVERABILITY; REFORMATION. In case any one or more of the provisions or parts of a provision contained in this Agreement shall, for any reason, be held to be invalid, illegal or unenforceable in any respect, such invalidity, illegality or unenforceability shall not affect any other provision or part of a provision of this Agreement; and this Agreement shall, to the fullest extent lawful, be reformed and construed as if such invalid or illegal or unenforceable provision, or part of a provision, had never been contained herein, and such provision or part reformed so that it would be valid, legal and enforceable to the maximum extent possible. Without limiting the foregoing, if any provision (or part of a provision) contained in this Agreement shall for any reason be held to be excessively broad as to duration, activity or subject, it shall be construed by limiting and reducing it, so as to be enforceable to the fullest extent compatible with then existing applicable law.

11. ASSIGNMENT. The Company shall have the right to assign its rights and obligations under this Agreement to a party which assumes the Company’s obligations hereunder. Consultant shall not have the right to assign his rights or obligations under this Agreement without the prior written consent of the Company. This Agreement shall be binding upon and inure to the benefit of the Consultant’s heirs and legal representatives in the event of his death or disability.

12. HEADINGS. Headings and subheadings are for convenience only and shall not be deemed to be a part of this Agreement.

13. AMENDMENTS. This Agreement may be amended or modified, in whole or in part, only by an instrument in writing signed by all parties hereto.

14. NOTICES. Any notices or other communications required hereunder shall be in writing and shall be deemed given when delivered in person or when mailed, by certified or registered first class mail, postage prepaid, return receipt requested, addressed to the parties at their addresses specified in the preamble to this Agreement or to such other addresses of which a party shall have notified the others in accordance with the provisions of this Section 14.

15. COUNTERPARTS. This Agreement may be executed in two or more counterparts, each of which shall constitute an original and all of which shall be deemed a single agreement.

16. GOVERNING LAW. This Agreement shall be construed in accordance with and governed for all purposes by the laws of the Commonwealth of Massachusetts applicable to contracts executed and wholly performed within such jurisdiction. Any dispute arising hereunder shall be referred to and heard in only a court located in Massachusetts.

17. SURVIVAL. The provisions of Sections 6 to 10 and 16 to 17 of this Agreement shall survive the expiration of the Term or the termination of this Agreement. This Agreement represents the entire agreement of the parties with respect to the subject matter of this Agreement and supersedes all prior agreements, written or oral, between the Company and the Consultant relating to the subject matter of this Agreement.

EXECUTED, under seal, effective as of the Effective Date.

Appendix “A”

(A) Duties and Responsibilities:

During the Term, the Consultant agrees to perform Services of up to no more than twenty (20) hours per month for the Company, as requested by the Company, including the following duties and tasks: Consultation in connection with the Company’s ongoing strategic collaboration with Novartis, and such other duties and responsibilities, reasonably consistent with his position, as may be designated from time to time by the Board. The Consultant shall also serve as a member of the Company’s Scientific Advisory Board.

(B) Scheduling and Completion and Termination Dates:

This agreement will be activated for the Term upon signing by both parties and can be renewed thereafter if mutually agreed upon.

(C) Fee Schedules and Payment Dates:

The Company agrees to pay the consultant a fee of $350.00 per hour for consulting requested by the Company. Invoices for hours of service should be sent monthly to the Company’s Chief Executive Officer or Chief Financial Officer. The Company may refuse to pay any invoices not provided to the Company within 60 days of the completion of Services.