EXHIBIT 23.1

CONSENT OF ERNST & YOUNG LLP, INDEPENDENT REGISTERED PUBLIC

ACCOUNTING FIRM

We consent to the incorporation by reference in the Registration Statements (Form S-3 No. 333-139641, Form S-8 Nos. 333-138248 and 333-145306) of Infinity Pharmaceuticals, Inc. and in the related Prospectuses of our reports dated March 11, 2008, with respect to the consolidated financial statements of Infinity Pharmaceuticals, Inc., and the effectiveness of internal control over financial reporting of Infinity Pharmaceuticals, Inc., included in this Annual Report (Form 10-K) for the year ended December 31, 2007.

/s/    Ernst & Young LLP

Boston, Massachusetts

March 11, 2008