Exhibit 4.1


 


NUMBER UNITS


U-[●]


 


SEE REVERSE FOR CERTAIN


DEFINITIONS


 


CUSIP 42588L 204


 


HENNESSY CAPITAL ACQUISITION CORP. III


 


UNITS CONSISTING OF ONE SHARE OF COMMON
STOCK AND ONE-HALF OF ONE WARRANT 

TO PURCHASE ONE SHARE OF COMMON STOCK


 


THIS CERTIFIES THAT                                         is
the owner of                     Units.


 


Each Unit (“Unit”)
consists of one (1) share of common stock, par value $0.0001 per share (“Common Stock”), of Hennessy
Capital Acquisition Corp. III, a Delaware corporation (the “Company”), and one-half of one warrant
(the “Warrant”). Each whole Warrant entitles the holder to purchase one share (subject to adjustment)
of Common Stock for $11.50 per share (subject to adjustment). Each Warrant will become exercisable on the later of (i) thirty
(30) days after the Company’s completion of a merger, capital stock exchange, asset acquisition, stock purchase, reorganization
or other similar business combination with one or more businesses (each a “Business Combination”),
or (ii) twelve (12) months from the closing of the Company’s initial public offering, and will expire unless exercised
before 5:00 p.m., New York City Time, on the date that is five (5) years after the date on which the Company completes its
initial Business Combination, or earlier upon redemption or liquidation (the “Expiration Date”). The
Common Stock and Warrants comprising the Units represented by this certificate are not transferable separately prior to             ,
20            , unless Credit Suisse Securities (USA) LLC elects to
allow separate trading earlier, subject to the Company’s filing of a Current Report on Form 8-K with the Securities and Exchange
Commission containing an audited balance sheet reflecting the Company’s receipt of the gross proceeds of the offering and
issuing a press release announcing when separate trading will begin. The terms of the Warrants are governed by a Warrant Agreement,
dated as of             , 2017, between the Company and Continental
Stock Transfer & Trust Company, as Warrant Agent, and are subject to the terms and provisions contained therein, all of
which terms and provisions the holder of this certificate consents to by acceptance hereof. Copies of the Warrant Agreement
are on file at the office of the Warrant Agent at 1 State Street Plaza, 30th Floor, New York, New York 10004, and
are available to any Warrant holder on written request and without cost.


 


This certificate is not valid unless countersigned
by the Transfer Agent and Registrar of the Company.


 


Witness the facsimile signature of its
duly authorized officers.


 


	 	 	 
	Secretary	 	President


 






    		 	 



     


    

 


Hennessy Capital Acquisition Corp. III


 


The Company will furnish
without charge to each unitholder who so requests, a statement of the powers, designations, preferences and relative, participating,
optional or other special rights of each class of stock or series thereof of the Company and the qualifications, limitations, or
restrictions of such preferences and/or rights.


 


The following abbreviations,
when used in the inscription on the face of this certificate, shall be construed as though they were written out in full according
to applicable laws or regulations:


 


	TEN COM	— 	as tenants in common	UNIF GIFT MIN ACT	—	                   
    Custodian
	 	 	 	 	 	 
	TEN ENT	— 	as tenants by the entireties	 	 	(Cust)
	 	 	 	 	 	(Minor)
	 	 	 	 	 	Under Uniform Gifts to Minors
	 	 	 	 	 
	JT TEN	— 	as joint tenants with right of survivorship and not as tenants in common	 	 	Act                      
 (State)


 


Additional abbreviations may also be used
though not in the above list.


 


For value received,              hereby
sell, assign and transfer unto                 


 


PLEASE INSERT SOCIAL SECURITY OR


OTHER


IDENTIFYING NUMBER OF ASSIGNEE


 


 


(PLEASE PRINT OR TYPEWRITE NAME AND ADDRESS,
INCLUDING ZIP CODE, OF ASSIGNEE)


  


	 	 	 	 	 
	 	 	 	 	 


 


                         
               Units represented by the within
Certificate, and do hereby irrevocably constitute and appoint


 


                        
                                         
    Attorney to transfer the said Units on the books of the within named Company with full power of
substitution in the premises.


 


Dated                     


 


	 	 	 
	 	 	Notice:  The signature to this assignment must correspond with the name as written upon the face of the certificate in every particular, without alteration or enlargement or any change whatever.
	Signature(s) Guaranteed:	 	 
	 	 	 
	THE SIGNATURE(S) MUST BE GUARANTEED BY AN ELIGIBLE GUARANTOR INSTITUTION (BANKS, STOCKBROKERS, SAVINGS AND LOAN ASSOCIATIONS AND CREDIT UNIONS WITH MEMBERSHIP IN AN APPROVED SIGNATURE GUARANTEE MEDALLION PROGRAM, PURSUANT TO S.E.C. RULE 17Ad-15(OR ANY SUCCESSOR RULE)).	 	 


 


In each case, as more fully described in
the Company’s final prospectus dated             , 2017, the
holder(s) of this certificate shall be entitled to receive a pro-rata portion of certain funds held in the trust account established
in connection with its initial public offering only in the event that (i) the Company redeems the shares of common stock sold in
its initial public offering and liquidates because it does not consummate an initial business combination by __________, 2019,
(ii) the Corporation redeems the shares of common stock sold in its initial public offering in connection with a stockholder vote
to approve an amendment to any provision of the Corporation’s amended and restated certificate of incorporation relating
to stockholders’ rights or pre-initial business combination activity, or (iii) if the holder(s) seek(s) to redeem for cash
his, her or its respective shares of common stock in connection with a tender offer (or proxy solicitation, solely in the event
the Company seeks stockholder approval of the proposed initial business combination) setting forth the details of a proposed initial
business combination. In no other circumstances shall the holder(s) have any right or interest of any kind in or to the trust account.