Exhibit 5.1

January 12, 2017

CBOE Holdings, Inc.

400 South LaSalle Street

Chicago, Illinois 60605

Re:                             $650,000,000 3.650% Senior Notes due 2027

Ladies and Gentlemen:

We refer to the Registration Statement on Form S-3, File No. 333-215401 (the “Registration Statement”) filed by CBOE Holdings, Inc., a Delaware corporation (the “Company”), with the Securities and Exchange Commission under the Securities Act of 1933, as amended (the “Securities Act”), which Registration Statement became effective upon filing pursuant to Rule 462(e) under the Securities Act. Pursuant to the Registration Statement, the Company is issuing $650,000,000 aggregate principal amount of the Company’s 3.650% Senior Notes due 2027 (the “Securities”). The Securities are being issued under an Indenture dated as of January 12, 2017 (the “Indenture”), between the Company and Wells Fargo Bank, National Association, as trustee (the “Trustee”). The Securities are to be sold by the Company pursuant to an underwriting agreement dated January 9, 2017 (the “Underwriting Agreement”) among the Company and Merrill Lynch, Pierce, Fenner & Smith Incorporated and Morgan Stanley & Co. LLC, as representatives of the several underwriters named in Schedule A to the Underwriting Agreement.

This opinion letter is being delivered in accordance with the requirements of Item 601(b)(5) of Regulation S-K under the Securities Act.

We have examined the Registration Statement, the Indenture, the Underwriting Agreement, the Securities in global form and the resolutions adopted by the board of directors of the Company relating to the Registration Statement, the Indenture, the Underwriting Agreement and the issuance of the Securities by the Company.

We have also examined originals, or copies of originals certified to our satisfaction, of such agreements, documents, certificates and statements of the Company and other corporate documents and instruments, and have examined such questions of law, as we have considered relevant and necessary as a basis for this opinion letter. We have assumed the authenticity of all documents submitted to us as originals, the genuineness of all signatures, the legal capacity of all persons and the conformity with the original documents of any copies thereof submitted to us for examination. As to facts relevant to the opinions expressed herein, we have relied without

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independent investigation or verification upon, and assumed the accuracy and completeness of, certificates, letters and oral and written statements and representations of public officials and officers and other representatives of the Company.

Based on and subject to the foregoing and the other limitations, qualifications and assumptions set forth herein, we are of the opinion that the Securities will constitute valid and binding obligations of the Company when the Securities are duly executed by duly authorized officers of the Company and duly authenticated by the Trustee, all in accordance with the provisions of the Indenture, and delivered to the purchasers thereof against payment of the agreed consideration therefor in accordance with the Underwriting Agreement.

Our opinion is subject to bankruptcy, insolvency, reorganization, moratorium, fraudulent conveyance, fraudulent transfer and other similar laws relating to or affecting creditors’ rights generally and to general equitable principles (regardless of whether considered in a proceeding in equity or at law), including concepts of commercial reasonableness, good faith and fair dealing and the possible unavailability of specific performance or injunctive relief.

This opinion letter is limited to the General Corporation Law of the State of Delaware and the laws of the State of New York (excluding the securities laws of the State of New York). We express no opinion as to the laws, rules or regulations of any other jurisdiction, including, without limitation, the federal laws of the United States of America or any state securities or blue sky laws.

We hereby consent to the filing of this opinion letter as an Exhibit to the Company’s Current Report on Form 8-K on the date hereof, which Form 8-K will be incorporated by reference into the Registration Statement, and to all references to our firm included in or made a part of the Registration Statement. In giving such consent, we do not thereby admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act.

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