Exhibit 5.1

September 10, 2012

CME Group Inc.

20 South Wacker Drive

Chicago, Illinois 60606

Ladies and Gentlemen:

We have acted as special counsel to CME Group Inc., a Delaware corporation (the “Company”), in connection with the public offering of $750,000,000 aggregate principal amount of the Company’s 3.00% Notes due 2022 (the “Securities”), to be issued under the Indenture, dated as of August 12, 2008 (the “Base Indenture”), between the Company and U.S. Bank National Association, as Trustee (the “Trustee”), as supplemented by the Fifth Supplemental Indenture, dated as of September 10, 2012 (the “Supplemental Indenture” and, together with the Base Indenture, the “Indenture”). On September 5, 2012, the Company entered into an Underwriting Agreement (the “Underwriting Agreement”) with Barclays Capital Inc., Merrill Lynch, Pierce, Fenner & Smith Incorporated and UBS Securities LLC, as representatives of the several underwriters named therein (the “Underwriters”), relating to the sale by the Company to the Underwriters of the Securities.

This opinion is being furnished in accordance with the requirements of Item 601(b)(5) of Regulation S-K under the Securities Act of 1933, as amended (the “Securities Act”).

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September 10, 2012

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In rendering the opinion stated herein, we have examined and relied upon the following:

(i) the registration statement on Form S-3 (File No. 333-163473) of the Company relating to the Securities and other securities of the Company filed with the Securities and Exchange Commission (the “Commission”) on December 3, 2009 under the Securities Act allowing for delayed offerings pursuant to Rule 415 of the General Rules and Regulations under the Securities Act (the “Rules and Regulations”), including information deemed to be a part of the registration statement pursuant to Rule 430B of the Rules and Regulations (such registration statement being hereinafter referred to as the “Registration Statement”);

(ii) an executed copy of the Underwriting Agreement;

(iii) the global certificates evidencing the Securities (the “Note Certificates”) in the form delivered by the Company to the Trustee for authentication and delivery;

(iv) an executed copy of the Base Indenture;

(v) an executed copy of the Supplemental Indenture;

(vi) a copy of the Company’s Fourth Amended and Restated Certificate of Incorporation, certified by the Secretary of State of the State of Delaware as of August 14, 2012 and certified by the Executive Director, Associate General Counsel and Assistant Corporate Secretary of the Company as of the date hereof;

(vii) a copy of the Company’s Eight Amended and Restated bylaws, as amended and in effect on the date hereof, certified by the Executive Director, Associate General Counsel and Assistant Corporate Secretary of the Company as of the date hereof; and

(viii) copies of certain resolutions of the Board of Directors of the Company, adopted on February 4, 2009 and May 24, 2012, each certified by the Executive Director, Asscociate General Counsel and Assistant Corporate Secretary of the Company as of the date hereof.

We have also examined originals or copies, certified or otherwise identified to our satisfaction, of such records of the Company and such agreements, certificates and receipts of public officials, certificates of officers or other representatives of the Company and others, and such other documents as we have deemed necessary or appropriate as a basis for the opinion stated below.

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September 10, 2012

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In our examination, we have assumed the genuineness of all signatures, including endorsements, the legal capacity and competency of all natural persons, the authenticity of all documents submitted to us as originals, the conformity to original documents of all documents submitted to us as facsimile, electronic, certified or photostatic copies, and the authenticity of the originals of such copies. As to any facts material to the opinion expressed herein that we did not independently establish or verify, we have relied upon statements and representations of officers and other representatives of the Company and others and of public officials.

We do not express any opinion with respect to the laws of any jurisdiction other than (i) the General Corporation Law of the State of Delaware (the “DGCL”) and (ii) the laws of the State of New York, and, to the extent that judicial or regulatory orders or decrees or consents, approvals, licenses, authorizations, validations, filings, recordings or registrations with governmental authorities are relevant, to those required under such laws (all of the foregoing being referred to as “Opined on Law”). We do not express any opinion as to the effect of any non-Opined on Law on the opinion stated herein.

The Indenture and the Note Certificates are referred to herein collectively as the “Transaction Agreements.”

Based upon the foregoing and subject to the limitations, qualifications, exceptions and assumptions stated herein, we are of the opinion that, when duly authenticated by the Trustee and issued and delivered by the Company against payment therefor in accordance with the terms of the Underwriting Agreement and the Indenture, the Securities will constitute valid and binding obligations of the Company entitled to the benefits of the Indenture and enforceable against the Company in accordance with their terms.

The opinion stated herein is subject to the following qualifications:

(a) the opinion stated herein is limited by applicable bankruptcy, insolvency, reorganization, moratorium, fraudulent transfer, preference and other similar laws affecting creditors’ rights generally, and by general principles of equity (regardless of whether enforcement is sought in equity or at law);

(b) we do not express any opinion with respect to the effect on the opinions stated herein of (i) the compliance or non-compliance of any party to any of the Transaction Agreements with any laws, rules or regulations applicable to such party or (ii) the legal status or legal capacity of any such party to any of the Transaction Agreements;

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(c) we do not express any opinion with respect to any law, rule or regulation that is applicable to any party to any of the Transaction Agreements or the transactions contemplated thereby solely because such law, rule or regulation is part of a regulatory regime applicable to such party or any of its affiliates as a result of the specific assets or business operations of such party or such affiliates;

(d) except to the extent expressly stated in the opinion contained herein, we have assumed that each of the Transaction Documents constitutes the valid and binding obligation of each party to such Transaction Document, enforceable against such party in accordance with its terms;

(e) we have assumed that the Trustee’s certificates of authentication of the Note Certificates will have been manually signed by one of the Trustee’s authorized officers and that the Note Certificates conform to the specimens thereof examined by us; and

(f) to the extent that any opinion relates to the enforceability of the choice of New York law and choice of New York forum provisions contained in any Transaction Agreement, such opinion is rendered solely in reliance upon New York General Obligations Law sections 5-1401 and 5-1402 and Rule 327(b) of New York Civil Practice Law and Rules and is subject to the qualification that such enforceability may be limited by, in each case, the terms of such sections 5-1401 and 5-1402, as well as by principles of public policy, comity or constitutionality.

In addition, in rendering the foregoing opinion, we have assumed that neither the execution and delivery by the Company of the Transaction Agreements and delivery by the Company of the Transaction Agreements nor the performance by the Company of its obligations under each of the Transaction Agreements: (i) constitutes or will constitute a violation of, or a default under, any lease, indenture, instrument or other agreement to which the Company or its property is subject, (ii) contravenes or will contravene any order or decree of any governmental authority to which the Company or its property is subject, (iii) violates or will violate any law, rule or regulation to which the Company or its property is subject or (iv) requires the consent, approval, licensing or authorization of, or any filing, recording or registration with, any governmental authority under any law, rule or regulation of any jurisdiction.

We hereby consent to the filing of this opinion with the Commission as an exhibit to the Company’s Current Report on Form 8-K being filed on the date hereof and incorporated by reference into the Registration Statement. We also hereby consent to the reference to our firm under the caption “Legal Matters” in the

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prospectus supplement dated September 5, 2012 and filed with the Commission. In giving this consent, we do not thereby admit that we are included in the category of persons whose consent is required under Section 7 of the Securities Act or the Rules and Regulations. This opinion is expressed as of the date hereof unless otherwise expressly stated, and we disclaim any undertaking to advise you of any subsequent changes in the facts stated or assumed herein or of any subsequent changes in applicable law.

Very truly yours,

/s/ Skadden, Arps, Slate, Meagher & Flom LLP