The Libertarian Party was founded in December 1971 and ran its first candidate for president in 1972.
Presidential candidate John Hospers and vice presidential candidate Theodora "Tonie" Nathan were on the ballot in two states. They received 1,111 votes in Colorado, 1,537 in Washington, and 43 write-in votes in Massachusetts for a total of 2,691. (I have seen elsewhere the total reported as 3,671.)
Hospers and Nathan made history when Republican presidential elector Roger MacBride refused to cast his electoral vote for Richard Nixon and instead voted for the Libertarians. This made Libertarian Tonie Nathan the first woman ever to receive an electoral vote.