Exhibit 23.1

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We consent to the incorporation by reference in the Registration Statements (Form S-8 No. 333-105236; Form S-8 No. 333-104804; Form S-8 No. 333-115656; Form S-8 No. 333-124497; Form S-3ASR No. 333-132554; and Form S-8 No. 333-14453) of CME Group Inc. of our reports dated February 29, 2008, with respect to the consolidated balance sheets of NYMEX Holdings, Inc. and subsidiaries as of December 31, 2007 and 2006, and the related consolidated statements of income, stockholders’ equity and cash flows for each of the years in the three-year period ended December 31, 2007, and the effectiveness of internal control over financial reporting as of December 31, 2007, which reports appears in the Form 8-K of CME Group Inc.

/s/ KPMG LLP

Chicago, Illinois

July 28, 2008