Exhibit 5.1

O   L   S   H   A   N 1325 AVENUE OF THE AMERICAS ● NEW YORK, NEW YORK 10019
TELEPHONE: 212.451.2300 ● FACSIMILE: 212.451.2222

March 27, 2019

PLx Pharma Inc.

8285 El Rio Street

Suite 130

Houston, Texas 77054

Re:           Registration Statement on Form S-3

Ladies and Gentlemen:

We have acted as counsel to PLx Pharma Inc., a Delaware corporation (the “Company”), in connection with the preparation and filing of a Registration Statement on Form S-3 (as may be amended from time to time, the “Registration Statement”) with the Securities and Exchange Commission under the Securities Act of 1933, as amended, relating to the offer and resale from time to time by the selling stockholders identified in the Prospectus constituting a part of the Registration Statement of an aggregate of up to 5,769,230 shares (the “Shares”) of the Company’s common stock, $0.001 par value per share, which have been authorized for issuance, and will be issued, to the selling stockholders named in the Registration Statement upon conversion of the 15,000 shares of the Company’s Series A Convertible Preferred Stock.

As a basis for rendering the opinion contained herein, we have examined the following documents: (i) the Registration Statement, (ii) the Amended Certificate of Incorporation (including the Amended and Restated Certificate of Designations, Preferences and Rights of Series A Convertible Preferred Stock) and the Amended and Restated Bylaws of the Company and (iii) certain resolutions adopted by the Board of Directors of the Company.  We have also examined and relied upon the original or certified copies of such records of the Company and such agreements, certificates of public officials, certificates of officers or representatives of the Company and others, and such other documents as we deem relevant and necessary as a basis for the opinion hereinafter expressed.  In such examination, we have assumed, without inquiry, the legal capacity of all natural persons, the authenticity of all documents submitted to us as originals, the genuineness of all signatures on original documents, the conformity with originals of all documents submitted to us as certified or photostatic copies, and the correctness of all statements of fact contained in the documents examined.  As to various questions of fact material to our opinion, we have relied upon statements or certificates of public officials, certificates of officers or representatives of the Company and others.

Based upon the foregoing and in reliance thereon and subject to the assumptions, qualifications and limitations set forth herein, we are of the opinion that the Shares have been duly authorized and, when issued in accordance with the terms of the Amended and Restated Certificate of Designations, Preferences and Rights of Series A Convertible Preferred Stock, will have been duly and validly issued, fully paid and non-assessable.

O L S H A N   F R O M E   W O L O S K Y   L L P WWW.OLSHANLAW.COM

March 27, 2019

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We are members of the Bar of the State of New York.  We express no opinion as to the effects of any laws, statutes, regulations or ordinances other than the laws of the States of New York and Delaware and the federal laws of the United States of America as in effect on the date of this letter, and we are expressing no opinion as to the effect of the laws of any other jurisdiction or as of any later date.

We hereby consent to the filing of this opinion as an exhibit to the Registration Statement and to the reference made to this firm under the caption “Legal Matters” in the prospectus constituting a part of the Registration Statement. In giving such consent, we do not thereby concede that this firm is within the category of persons whose consent is required under Section 7 of the Securities Act of 1933, as amended, or the rules and regulations of the Securities and Exchange Commission.

This opinion letter is limited to the matters set forth herein, and no opinion may be inferred or implied beyond the matters expressly set forth herein.  This opinion letter is not a guaranty nor may one be inferred or implied.  This opinion letter speaks as of the date hereof and we assume no obligation to update or supplement this opinion letter to reflect any facts or circumstances that may hereafter come to our attention or any changes in fact or law that may hereafter occur.

Very truly yours,

/s/ OLSHAN FROME WOLOSKY LLP

OLSHAN FROME WOLOSKY LLP