Exhibit 5.1

Transgenomic, Inc.
12325 Emmet Street

Omaha, NE 68164

Ladies and Gentlemen:

We have acted as counsel to Transgenomic, Inc., a Delaware corporation (the “Company”), in connection with the offering of an aggregate of 3,573,899 shares (the “Shares”), of the Company’s common stock, par value $0.01 per share (the “Common Stock”), together with warrants (the “Warrants”) to purchase up to an additional 714,780 shares of Common Stock (the “Warrant Shares”), all pursuant to the Registration Statement on Form S-3 (File No. 333-201907) originally filed with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Act”), on February 6, 2015 (the “Registration Statement”), the related prospectus dated February 5, 2015, included in the Registration Statement (the “Base Prospectus”), and the prospectus supplement to be filed with the Commission pursuant to Rule 424(b) of the rules and regulations of the Act (the “Prospectus Supplement”). The Base Prospectus and the Prospectus Supplement are collectively referred to as the “Prospectus.” The Company has requested our opinion in connection with certain related matters.

In connection with this opinion, we have examined and relied upon the Registration Statement, the Prospectus, the form of Warrant to be filed as an exhibit to the Company’s Current Report of the Company on Form 8-K, the Company’s Certificate of Incorporation and Company’s Bylaws, each as currently in effect, and the originals or copies certified to our satisfaction of such records, documents, certificates, memoranda and other instruments as in our judgment are necessary or appropriate to enable us to render the opinion expressed below. As to certain factual matters, we have relied upon a certificate of an officer of the Company and have not independently verified such matters. We have assumed the genuineness and authenticity of all documents submitted to us as originals, and the conformity to originals of all documents submitted to us as copies thereof.

With regard to our opinion concerning the Warrants and the Warrant Shares, we express no opinion to the extent that, notwithstanding its current reservation of shares of Common Stock, future issuances of securities by the Company, including the Warrant Shares, and/or antidilution adjustments to outstanding securities of the Company, including the Warrants, may cause the Warrants to be exercisable for more shares of Common Stock than the number that remain authorized but unissued.

Our opinion is limited to the matters stated herein and no opinion is implied or may be inferred beyond the matters expressly stated. Our opinion herein is expressed solely with respect to the federal laws of the United States, the General Corporation Law of the State of Delaware and, as to the Warrants constituting valid and legally binding obligations of the Company, the laws of the State of New York. We are not rendering any opinion as to compliance with any federal or state antifraud law, rule or regulation relating to securities, or to the sale or issuance thereof. Our opinion is based on these laws as in effect on the date hereof, and we disclaim any obligation to advise you of facts, circumstances, events or developments which hereafter may be brought to our attention and which may alter, affect or modify the opinion expressed herein. We express no opinion as to whether the laws of any particular jurisdiction other than those identified above are applicable to the subject matter hereof.

On the basis of the foregoing, and in reliance thereon, we are of the opinion that (i) the Shares, when sold and issued against payment therefor in accordance with the Registration Statement and the Prospectus, will be validly issued, and the Shares fully paid and nonassessable, (ii) provided that the Warrants have been duly executed by the Company and duly delivered to the purchasers thereof against payment therefor, the Warrants, when issued and sold as contemplated in the Registration Statements and the Prospectus will be binding obligations of the Company, enforceable against the Company in accordance with their terms, except as enforcement thereof may be limited by bankruptcy, insolvency, fraudulent transfer, reorganization, moratorium or other similar laws relating to or affecting creditors’ rights generally and by general equitable principles and limitations on availability of equitable relief, including specific performance (regardless of whether such enforceability is considered in a proceeding at law or in equity), and (iii) the Warrant Shares, when issued and paid for in accordance with the terms of the Warrants, will be validly issued, fully paid and nonassessable.

We consent to the reference to our firm under the caption “Legal Matters” in the Prospectus included in the Registration Statements and to the filing of this opinion as an exhibit to a Current Report of the Company on Form 8-K.

Very truly yours,

/s/ Paul Hastings LLP