Exhibit 5.1

[Jones Walker Letterhead]

March 12, 2012

CenturyLink, Inc.

100 CenturyLink Drive

Monroe, Louisiana 71203

Ladies and Gentlemen:

We have acted as special counsel for CenturyLink, Inc., a Louisiana corporation (the “Company”), in connection with the issuance and sale of $1,400,000,000 aggregate principal amount of 5.80% Senior Notes, Series T, due 2022 and $650,000,000 aggregate principal amount of 7.65% Senior Notes, Series U, due 2042 (collectively, the “Notes”), pursuant to the Underwriting Agreement, dated as of March 5, 2012 (the “Underwriting Agreement”), entered into by and among the Company and Barclays Capital Inc., J.P. Morgan Securities LLC, Morgan Stanley & Co. LLC, RBC Capital Markets, LLC and the other underwriters named in Schedule I therein, as underwriters (collectively, the “Underwriters”). The Notes will be issued pursuant to the Indenture, dated as of March 31, 1994 (the “Original Indenture”), by and between the Company and Regions Bank (successor to Regions Bank of Louisiana and First American Bank & Trust of Louisiana), as trustee (the “Trustee”), as heretofore supplemented by board resolutions and as further supplemented by supplemental indentures, including the Seventh Supplemental Indenture dated as of March 12, 2012 by and between the Company and the Trustee (the “Supplemental Indenture” and, together with the Original Indenture, as so supplemented through the date hereof, the “Indenture”).

In connection with the opinion expressed herein, we have examined such documents, records and matters of law as we have deemed relevant or necessary for purposes of such opinion. In conducting our examination, we have assumed without verification the legal capacity of all natural persons, 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 certified, conformed or photostatic copies, the authenticity of the originals of such copies, the due authorization, execution and delivery of all documents by all parties other than the Company, and the validity, binding effect and enforceability thereof on all such parties. As to various questions of fact material to this opinion, we have relied without independent verification upon (i) the accuracy of certificates and other comparable documents of officers and representatives of the Company, (ii) representations and warranties made by the Company in the Underwriting Agreement (other than representations and warranties as to legal matters that are the subject of this opinion), (iii) statements made to us in discussions with the Company’s management and (iv) certificates of public officials.

Based on the foregoing, and subject to the further limitations, qualifications and assumptions set forth herein, we are of the opinion that the Notes, when they are duly authenticated by the Trustee in accordance with the Indenture and issued and delivered to the Underwriters against payment therefor in accordance with the terms of the Underwriting

CenturyLink, Inc.

March 12, 2012

Page 2 of 2

Agreement, will constitute valid and binding obligations of the Company.

For purposes of the opinion expressed herein, we have assumed that (i) the definitive terms of the Notes will be established in accordance with the provisions of the Indenture, (ii) the Trustee has duly authorized, executed and delivered the Original Indenture and the Supplemental Indenture, and is qualified under the Trust Indenture Act of 1939, and (iii) the Indenture is the valid, binding and enforceable obligation of the Trustee.

The opinion expressed herein is subject to the qualification that enforceability may be limited by (i) applicable bankruptcy, insolvency, fraudulent transfer, reorganization, moratorium or similar laws of general applicability relating to or affecting the enforcement of creditors’ rights, (ii) general principles of equity (regardless of whether enforceability is considered in a proceeding in equity or at law), (iii) public policy considerations that may limit the rights of parties to obtain certain remedies and (iv) governmental authority to limit, delay or prohibit the making of payments outside of the United States or in a foreign currency or currency unit.

We do not express any opinion herein concerning any law other than the Louisiana Business Corporation Law (including the statutory provisions and reported judicial decisions interpreting the foregoing). We express no opinion as to the application of the securities or blue sky laws of the various states to the sale of the Notes.

This letter has been furnished in accordance with applicable rules promulgated by the Securities and Exchange Commission (the “Commission”), and is expressly limited to the specific issues addressed herein. We render no opinion, whether by implication or otherwise, as to any other matter relating to the Company, the Indenture, the Notes or any of the other transactions discussed hereunder. This letter speaks only as of the date hereof. We assume no obligation to revise or supplement this letter should the presently applicable laws be changed by legislative action, judicial decision or otherwise.

We consent to the filing of this letter as Exhibit 5.1 to the Current Report on Form 8-K dated the date hereof filed by the Company and incorporated by reference into the Company’s Registration Statement on Form S-3 (Registration No. 333-179888) (the “Registration Statement”), and to the reference to Jones, Walker, Waechter, Poitevent, Carrère & Denègre, L.L.P., New Orleans, Louisiana, under the caption “Legal Matters” in the prospectus supplement dated March 5, 2012 describing the Notes and constituting a part of such Registration Statement. In giving this consent, we do not admit that we are within the category of persons whose consent is required under Section 7 of the Act or the general rules and regulations of the Commission.

Very truly yours,

/s/ Jones, Walker, Waechter, Poitevent,
Carrère & Denègre, L.L.P.

JONES, WALKER, WAECHTER, POITEVENT,
CARRÈRE & DENÈGRE, L.L.P.