Exhibit 8.1

CME Group Inc.

20 S. Wacker Drive

Chicago, IL 60606

Ladies and Gentlemen:

We have acted as special U.S. tax counsel to CME Group, Inc., a Delaware corporation (“CME”), in connection with the preparation and filing of the Registration Statement No. 333-199429 on Form S-4, which includes the Prospectus of CME Group Inc. and Proxy Statement of GFI Group Inc., dated as of December 24, 2014 (the “Prospectus”), and the supplement thereto, dated as of January 22, 2015 (the “Supplement”), filed with the Securities and Exchange Commission in connection with the acquisition, by CME, of all of the common shares of GFI Group, Inc., a Delaware corporation (“GFI”), in exchange for common shares of CME, with cash paid in lieu of fractional shares, pursuant to the Agreement and Plan of Merger, dated July 30, 2014 and as amended by Amendment No. 1, dated as of December 2, 2014, Amendment No. 2, dated as of January 15, 2015, and Amendment No. 3, dated as of January 22, 2015 (the “Agreement”), by and among CME, GFI, Commodore Acquisition Corp., a Delaware corporation and a wholly-owned CME Subsidiary (“Merger Sub 1”), and Commodore Acquisition LLC, a Delaware limited liability company and a wholly-owned CME Subsidiary (“Merger Sub 2”).(1) Pursuant to the Agreement, (i) Merger Sub 1 will merge with and into GFI, with GFI surviving (the “Merger”), and (ii) immediately thereafter and as part of an integrated transaction, GFI will merge with and into Merger Sub 2, with Merger Sub 2 surviving (the “Subsequent Merger” and, together with the Merger, the “Combination”).

(1)         Unless otherwise defined, capitalized terms used in this opinion have the meanings assigned to them in the Agreement.

In connection with our opinion, we have reviewed originals or copies, certified or otherwise identified to our satisfaction, of the Agreement, the Supplement, the Prospectus (prepared with respect to the Combination) and such other documents, certificates and records as we have deemed necessary or appropriate as a basis for the opinion set forth below.  We have assumed that the Combination will be consummated in accordance with the Agreement, the Supplement, the Prospectus and such other documents, certificates and records.

For purposes of our opinion, we have assumed the legal capacity of all natural persons, the genuineness of all signatures, the authenticity of all documents submitted to us as originals, the conformity to original documents of all documents submitted to us as certified, conformed, electronic or photostatic copies and the authenticity of the originals of such latter documents.  We have assumed that such documents, certificates and records are duly authorized, valid and enforceable.

In rendering our opinion, we have also relied upon statements and representations of officers and other representatives of CME, Merger Sub 1, Merger Sub 2 and GFI, including factual statements and representations set forth in officers’ certificates dated the date hereof from officers of CME, Merger Sub 1, Merger Sub 2 and GFI (the “Representation Letters”) and have assumed that such statements and representations are and will continue to be correct as of the Effective Time without regard to any qualification as to knowledge or belief. Our opinion assumes and is expressly conditioned on, among other things, the initial and continuing accuracy and completeness of the facts, information, representations, covenants and agreements set forth in the documents referred to above and the statements, representations, covenants and agreements made by CME, Merger Sub 1, Merger Sub 2 and GFI, including those set forth in the Representation Letters, and we have assumed (i) that the Representation Letters will be re-executed by appropriate officers, and that we will render our opinion pursuant to sections 7.02(c) of the Agreement, as of the Effective Time, and (ii) that there will be no change in law between the date hereof and the Effective Time.

In rendering our opinion, we have relied on the Internal Revenue Code of 1986, as amended (the “Code”), Treasury Regulations, judicial authorities, published positions of the Internal Revenue Service (the “Service”) and such other authorities as we have considered relevant, all as in effect as of the date of this opinion and all of which are subject to differing interpretations or change at any time (possibly with retroactive effect).  A change in the authorities upon which our opinion is based, or any variation or difference in any fact from those set forth or assumed herein or in the Supplement, the Prospectus, the Agreement or the Representation Letters, could affect our conclusions.  An opinion of counsel is not binding on the Service or any court.  No assurance can be given that the Service would not assert, or that a court would not sustain, a position contrary to this opinion.

Based upon and subject to the foregoing, we are of the opinion that, under current U.S. federal income tax law, the Combination will be treated as a reorganization within the meaning of section 368(a) of the Code.

Except as set forth above, we express no other opinion.  This opinion is furnished to you solely for your benefit in connection with the Combination and is not to be relied upon by

anyone else without our prior written consent.  This opinion is expressed as of the date hereof, and we are under no obligation to supplement or revise our opinion to reflect any legal developments or factual matters arising subsequent to the date hereof or the impact of any information, document, certificate, record, statement, representation, covenant, or assumption relied upon herein that becomes incorrect or untrue.