CME (CME) 10-K 2004 FY Annual report

Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

We consent to the incorporation by reference in the following Registration Statements:

(1) Registration Statement (Form S-8 No. 333-105236) pertaining to the Amended and Restated Omnibus Stock Plan of Chicago Mercantile Exchange Holdings Inc., and

(2) Registration Statement (Form S-8 No. 333-104804; Form S-8 No. 333-115656) pertaining to the Agreement between Chicago Mercantile Exchange Holdings Inc. and James J. McNulty;

of our reports dated February 11, 2005, with respect to the consolidated financial statements of Chicago Mercantile Exchange Holdings Inc., Chicago Mercantile Exchange Holdings Inc. management’s assessment of the effectiveness of internal control over financial reporting, and the effectiveness of internal control over financial reporting of Chicago Mercantile Exchange Holdings Inc., incorporated by reference in this Annual Report (Form 10-K) for the year ended December 31, 2004, and our report included in the following paragraph with respect to the financial statement schedules of Chicago Mercantile Exchange Holdings Inc. included in this Annual Report (Form 10-K) for the year ended December 31, 2004.

Our audits also included the financial statement schedules of Chicago Mercantile Exchange Holding Inc. listed in Item 15(a). These schedules are the responsibility of Chicago Mercantile Exchange Holding Inc.’s management. Our responsibility is to express an opinion based on our audits. In our opinion, as to which the date is February 11, 2005, the financial statement schedules referred to above, when considered in relation to the basic financial statements taken as a whole, present fairly in all material respects the information set forth therein.

/s/ Ernst & Young LLP

Chicago, Illinois

March 10, 2005