Exhibit 5.1

[Letterhead of Wachtell, Lipton, Rosen & Katz]

March 27, 2020

CapStar Financial Holdings, Inc.

1201 Demonbreun Street, Suite 700

Nashville, Tennessee 37203

Re: Registration Statement on Form S-4 Relating to (i) the Agreement and Plan of Merger, dated as of January 23, 2020, by and between CapStar Financial Holdings, Inc. and FCB Corporation and (ii) Plan of Bank Merger, dated as of January 23, 2020, by and between CapStar, CapStar Bank and The Bank of Waynesboro.

Ladies and Gentlemen:

We have acted as counsel to CapStar Financial Holdings, Inc., a Tennessee corporation (“CapStar”), in connection with the Registration Statement on Form S-4 (as amended, the “Registration Statement”, which term does not include any other document or agreement whether or not specifically referred to therein or attached as an exhibit or schedule thereto) filed with the U.S. Securities and Exchange Commission (the “Commission”), relating to the registration under the Securities Act of 1933, as amended (the “Securities Act”), of up to 3,634,218 shares of common stock, par value $1.00 per share, of CapStar (the “Shares”) to be issued in connection with the transactions contemplated by (i) the Agreement and Plan of Merger, dated as of January 23, 2020 (as it may be amended from time to time, the “FCB Merger Agreement”), by and between CapStar and FCB Corporation and (ii) the Plan of Bank Merger, dated as of January 23, 2020 (as it may be amended from time to time, the “BOW Merger Agreement”), by and among CapStar, CapStar Bank and The Bank of Waynesboro. CapStar is filing the Registration Statement with the Commission with respect to the Shares. This opinion is provided pursuant to the requirements of Item 21(a) of Form S-4 and Item 601(b)(5) of Regulation S-K.

In rendering this opinion, we have examined the Registration Statement, the FCB Merger Agreement, the BOW Merger Agreement and such corporate records, other documents and matters of law as deemed necessary or appropriate. In this opinion, we have relied, with your consent, upon oral and written representations of officers of CapStar and certificates of officers of CapStar and public officials with respect to the accuracy of the factual matters addressed in such representations and certificates. In addition, in rendering this opinion, we have assumed without verification the genuineness of all signatures, the authenticity of all documents submitted to us as originals, the conformity of certified copies submitted to us with the original documents to which such certified copies relate and the legal capacity of all individuals executing any of the foregoing documents.

Based on and subject to the foregoing examination and in reliance thereon, and subject to the qualifications, assumptions and limitations stated herein, we are of the opinion that the Shares are or will be, upon issuance, duly authorized and, when the Registration Statement has been declared effective by order of the Commission and paid for upon the terms and conditions set forth in the Registration Statement and the FCB Merger Agreement or the BOW Merger Agreement, as applicable, the Shares will be validly issued, fully paid and nonassessable.

The opinion set forth above is subject to the effects of (a) bankruptcy, insolvency, fraudulent conveyance, reorganization, moratorium and other similar laws relating to or affecting the enforcement of creditors’ rights generally, (b) general equitable principles (whether considered in a proceeding in equity or at law) and (c) an implied covenant of good faith and fair dealing. We express no opinion as to whether, or the extent to which, the laws of any particular jurisdiction apply to the subject matter hereof.

This opinion is delivered as of the date hereof, and we undertake no obligation to advise you of any changes in applicable law or any other matters that may come to our attention after the date hereof.

We hereby consent to the filing of this opinion as Exhibit 5.1 to the Registration Statement and the references to our name therein, as well as under the heading “Legal Matters” in the related prospectus. In giving this consent, we do not thereby admit that we are within the category of persons whose consent is required by Section 7 of the Securities Act or the rules and regulations of the Commission thereunder.

Very truly yours,

/s/ Wachtell, Lipton, Rosen & Katz