The Libertarian Party in the United States was founded on December 11, 1971. The Libertarian slogan “Legalize freedom” has been cited in print since at least 1974; “Legalize freedom — vote Libertarian!” has been cited in print since at least 1992. The party slogan (not trademarked) has been printed on many bumper stickers.
 
     
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Newsweek
Volume 84, Issues 19-27
1974
Pg. 207:
Anarchic as it sounds, Libertarianism has surfaced in this election year as an ideology matched to the mood of many disgruntled Americans. The party’s slogan, “Legalize Freedom,” gives Libertarians a unique appeal to radicals on both the right and left.
 
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28 October 1974, Harlan Daily Enterprise, “On Libertarianism For Middle Class” by Nicholas Van Hoffman, pg. 4, col. 4:
“Legalize Freedom,” is one of their slogans, which all those lumpy, gray men running for the Democratic Presidential nomination will assent to as long as they don’t have to apply it.
 
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13 November 1975, The Deseret News (Salt Lake City, UT), pg. B9, col. 1:
Spot on state ballot
(...)
OGDEN (UPI)—The Utah Libertarian Party has secured a place on the state’s ballot and named a candidate for the U.S. Senate.
(...)
Andrews, president of the Trotter for Senate Committee, said the theme of the campaign would be “Legalize Freedom.” He said the slogan “epitomized the Libertarian philosophy which calls for the repeal of all victimless crime laws, supports a laissez faire economic policy and advocates a non-interventionist foreign policy.”
 
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26 May 1982, Nashua (NH) Telegraph, “Lampooning an overregulated society to bring about change” by Al Martinez (Los Angeles Times), pg. 34, col. 5:
“And how about this,” Lowdermilk says as he reaches into a briefcase with a bumper sticker on it that says “legalize freedom.”
(Dale Lowdermilk, a libertarian—ed.)
 
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8 September 1986, The Ledger (Lakeland, FL), “The Plight Of The Libertarian,” pg. 6A, col. 3:
I’d like to urge everyone to legalize freedom by voting Libertarian, but since you can’t in Florida, allow me to suggest voting “none of the above is acceptable.” What’s that? Florida doesn’t allow that either?
(...)
KEITT T. MILLER
Lakeland
 
Google Books
Healing Our World:
The Other Piece of the Puzzle
By Mary J. Ruwart
Kalamazoo, MI: SunStar Press
1992
Pg. 277:
Legalize freedom — vote Libertarian!
—slogan of the Libertarian Party, U.S.A.
 
22 August 2002, The Arizona Daily Star (Tucson, AZ), “A low-key fight for strong Libertarian views”:
He saw a driver with a “Legalize Freedom, Vote Libertarian” bumper sticker, ...
 
Google Books
Healing Our World in an Age of Aggression
By Mary J. Ruwart
Kalamazoo, MI : SunStar Press
2003
Pg., 374:
Legalize freedom— vote Libertarian! —slogan of the Libertarian Party, U.S.A.