Exhibit 32.1

Certification of CEO and CFO Pursuant to

18 U.S.C. Section 1350,

as Adopted Pursuant to

Section 906 of the Sarbanes-Oxley Act of 2002

In connection with the Quarterly Report on Form 10-Q of CME Group Inc. (the “Company”) for the quarter ended September 30, 2008 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), Craig S. Donohue, as Chief Executive Officer of the Company, and James E. Parisi, as Chief Financial Officer of the Company, each hereby certifies, pursuant to 18 U.S.C. § 1350, as adopted pursuant to § 906 of the Sarbanes-Oxley Act of 2002, that, to the best of his knowledge:

(1) The Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

(2) The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

/s/ Craig S. Donohue

Name:     Craig S. Donohue

Title:      Chief Executive Officer

Date: November 10, 2008

/s/ James E. Parisi

Name:     James E. Parisi

Title:      Chief Financial Officer

Date: November 10, 2008

This certification accompanies the Report pursuant to § 906 of the Sarbanes-Oxley Act of 2002 and shall not, except to the extent required by the Sarbanes-Oxley Act of 2002, be deemed filed by the Company for purposes of §18 of the Securities Exchange Act of 1934, as amended.

A signed original of this written statement required by § 906 of the Sarbanes-Oxley Act of 2002 has been provided to the Company and will be retained by the Company and furnished to the Securities and Exchange Commission or its staff upon request.