Exhibit 5.1

May 30, 2017

Hennessy Capital Acquisition Corp. III

3485 N. Pines Way, Suite 110

Wilson, Wyoming 83014 

Re:    Registration Statement of Hennessy Capital Acquisition Corp. III

Ladies and Gentlemen:

We have acted as counsel to Hennessy Capital Acquisition Corp. III, a Delaware corporation (the “Company”) in connection with the registration by the Company with the United States Securities and Exchange Commission of up to 25,875,000 units of the Company, including the underwriters’ over-allotment option (collectively the “Units”), with each Unit consisting of one share of common stock, par value $0.0001 per share (the “Common Stock”) of the Company and one-half of one warrant of the Company, each whole warrant to purchase one share of Common Stock (the “Warrant”), pursuant to a Registration Statement on Form S-1 initially filed by the Company with the Commission on May 30, 2017 (as amended, the “Registration Statement”).

We have examined such documents and considered such legal matters as we have deemed necessary and relevant as the basis for the opinion set forth below. With respect to such examination, we have assumed 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 reproduced or certified copies, and the authenticity of the originals of those latter documents. As to questions of fact material to this opinion, we have, to the extent deemed appropriate, relied upon certain representations of certain officers and employees of the Company.

Based upon the foregoing, we are of the opinion that:

1.           Units. When the Registration Statement becomes effective under the Securities Act of 1933, as amended (the “Act”) and when the offering is completed as contemplated by the Registration Statement, such Units will be validly issued, fully paid and non-assessable.

2.           Common Stock. When the Registration Statement becomes effective under the Act and when the offering is completed as contemplated by the Registration Statement, the shares of Common Stock will be validly issued, fully paid and non-assessable.

3.           Warrants. When the Registration Statement becomes effective under the Act, when the warrant agreement under which the Warrants are to be issued (the “Warrant Agreement”) is duly executed and delivered, and when the Warrants underlying the Units are issued, delivered and paid for as part of the Units, as contemplated by the Registration Statement, such Warrants will be validly issued, fully paid and non-assessable and will be legally binding obligations of the Company enforceable in accordance with their terms except: (a) as such enforceability may be limited by bankruptcy, insolvency, reorganization or similar laws affecting creditors’ rights generally and by general equitable principles (regardless of whether enforceability is considered in a proceeding in equity or at law); (b) as enforceability of any indemnification or contribution provision may be limited under the federal and state securities laws, and (c) that the remedy of specific performance and injunctive and other forms of equitable relief may be subject to the equitable defenses and to the discretion of the court before which any proceeding therefor may be brought.

We are opining solely on all applicable statutory provisions of Delaware corporate law, including the rules and regulations underlying those provisions, all applicable provisions of the Delaware Constitution, all applicable judicial and regulatory determinations in connection therewith and, as to the Units and the Warrants constituting legally binding obligations of the Company, solely with respect to the laws of the State of New York. Our opinion is based on these laws as in effect on the date hereof and as of the effective date of the Registration Statement, and we assume no obligation to revise or supplement this opinion after the effective date of the Registration Statement should the law be changed by legislative action, judicial decision, or otherwise. We express no opinion as to whether the laws of any other jurisdiction are applicable to the subject matter hereof. We are not rendering any opinion as to compliance with any other federal or state law, rule or regulation relating to securities, or to the sale or issuance thereof.

We hereby consent to the use of this opinion as an exhibit to the Registration Statement, to the use of our name as your counsel and to all references made to us in the Registration Statement and in the prospectus forming a part thereof.  In giving this consent, we do not hereby admit that we are in the category of persons whose consent is required under Section 7 of the Act, or the rules and regulations promulgated thereunder.