September 20, 2018

Nicholas A. Petruska
Executive Vice President, Chief Financial Officer and Secretary
Hennessy Capital Acquisition Corp. III
3845 North Pine Way
Suite 110
Wilson, WY 83014

       Re: Hennessy Capital Acquisition Corp. III
           Revised Preliminary Proxy Statement
           Filed September 5, 2018
           File No. 1-38119

Dear Mr. Petruska:

       We have reviewed your filing and have the following comments. In some of
our
comments we may ask you to provide us information so that we may better
understand your
disclosure.

        Please respond to these comments within 10 business days by providing
the requested
information or advise us as soon as possible when you will respond. If you do
not believe
that our comments apply to your facts and circumstances, please tell us why in
your response.

       After reviewing your response to these comments, we may have additional
comments.

Revised Preliminary Proxy Statement on Schedule 14A filed September 5, 2018

NRC Group Business Overview, page 23

1.    You disclose here and on page 151 that NRC Group's historical combined
net loss was
      $2.3 million for the six months ended June 30, 2018; however, NRC Group's
historical
      combined net loss for the six months ended June 30, 2018 was actually
$569,000 per page
      F-30. Please explain to us the reasons for the differing amounts or
otherwise address any
      disclosure discrepancy accordingly.
Hennessy Capital Management's Discussion and Analysis of Financial Condition
and Results of
Operations
Results of Operations, page 147
 Nicholas A. Petruska
FirstNameCapital Acquisition Corp. III
Hennessy LastNameNicholas A. Petruska
Comapany 20, 2018
September NameHennessy Capital Acquisition Corp. III
September 20, 2018 Page 2
Page 2
FirstName LastName
2.       You disclose on page 148 that cash used in operations for the six
months ended June 30,
         2018 was approximately $471,000; however, cash used in operations for
the six months
         ended June 30, 2018 was actually $1,387,000 per page F-5. Please
explain to us the
         reasons for the differing amounts or otherwise address any disclosure
discrepancy
         accordingly.
NRC Group's Management's Discussion and Analysis of Financial Condition and
Results of
Operations
NRC Group Liquidity and Capital Resources, page 182

3.       Please ensure that your discussion of net cash provided by operating
activities for the six
         months ended June 30, 2018 agrees to the changes as depicted in your
statement of cash
         flows. For example, your disclosure indicates that there were
increases in accounts
         payable and accounts receivable; however, per page F-32, it appears
that both accounts
         payable and accounts receivable may have actually decreased during the
six months ended
         June 30, 2018.
Financial Statements of Progressive Environmental Services, Inc.
Independent Auditor's Report, page F-74

4.       You disclose on page 81 that the acquisition of Progressive
Environmental Services, Inc.
         meets the threshold for reporting of significant acquired businesses.
You further disclose
         on page 223 that the audited financial statements of Progressive
Environmental Services,
         Inc. as of December 31, 2017 and for the year then ended have been so
included in
         reliance on the report of Jaynes, Reitmeier, Boyd & Therrell, P.C. We
note the related
         audit report on page F-74 states that the financial statements of
Progressive Environmental
         Services, Inc. for the year ended December 31, 2016 were audited by
another auditor who
         expressed an unmodified opinion on those statements on June 23, 2017.
Please tell us
         what consideration you gave to presenting the audit report for the
financial statements of
         Progressive Environmental Services, Inc. for the year ended December
31, 2016.
        We remind you that the company and its management are responsible for
the accuracy
and adequacy of their disclosures, notwithstanding any review, comments,
action, or absence of
action by the staff.

        You may contact Jeffrey R. Gordon, Staff Accountant, at (202) 551-3866
or Kevin W.
Stertzel, Staff Accountant, at (202) 551-3723 if you have questions regarding
comments on the
financial statements and related matters. Please contact Edward M. Kelly,
Senior Counsel, at
(202) 551-3728 or Amanda Ravitz, Assistant Director, at (202) 551-3412 with any
other
questions.



                                                              Sincerely,
 Nicholas A. Petruska
Hennessy Capital Acquisition Corp. III
September 20, 2018
Page 3

FirstName LastNameNicholas A. Petruska
                                                      Division of Corporation
Finance
Comapany NameHennessy Capital Acquisition Corp. III
                                                      Office of Manufacturing
and
September 20, 2018 Page 3                             Construction
FirstName LastName