May 8, 2018

VIA EDGAR

Securities and Exchange Commission

Division of Corporation Finance

100 F Street, N.E.

Washington, D.C. 20549

Registration Statement on Form S-3 (File No. 333-224545)

Request for Acceleration

Ladies and Gentlemen:

Pursuant to Rule 461 promulgated under the Securities Act of 1933, as amended, Infinity Pharmaceuticals, Inc. (the “Registrant”) hereby requests acceleration of the effective date of its Registration Statement on Form S-3 (File No. 333-224545), so that it may become effective at 4:00 p.m. Eastern time on May 10, 2018, or as soon thereafter as practicable or at such later time as the Registrant may orally request via telephone call to the staff.