Over the decades, while LIFE magazine published dozens of photo essays by the 20th century’s greatest photographers, few combined the raw intensity and technical brilliance of Larry Burrows’ seminal “One Ride With Yankee Papa 13″ — widely seen as the single greatest photographic achievement to emerge from the war in Vietnam.

Here, LIFE presents “One Ride With Yankee Papa 13″ in its entirety for the first time since it was published: all the photos that appeared in the April 16, 1965 issue of LIFE are here; all of the words here, from the third slide onward, are taken directly from that issue.

In his searing, deeply sympathetic portrait of young men fighting for their lives at the very moment America is ramping up its involvement in Southeast Asia, Burrows’ work anticipates the scope and the dire, calamitous arc of the entire war in Vietnam.