Last Thoughts on Woody Guthrie was performed by Bob Dylan at New York Town Hall on Friday, April 12, 1963. It is included on the The Bootleg Series, Vol. 1, Track 22.

Woody Guthrie was an inspiration and hero to the young Dylan, and the reason Dylan came to New York City in the first place:

In the early 1960s a young folksinger named Robert Zimmerman borrowed a copy of Bound for Glory from a prof at the University of Minnesota. Having established himself as a Woody Guthrie jukebox and having learned that Guthrie was dying, he hitch-hiked east and made himself at home with the remaining Guthries.
-Woody Guthrie by icicle
Dylan met Guthrie for the first time in early 1961 as Woody lay in a New Jersey hospital suffering from Huntington's Chorea. This was the very beginning of Dylan's career: Song for Woody, his first recorded original composition, was written one month later, and about eight weeks after that he gave his first paid performance.

Two years later, he was giving one of his first major performances at New York Town Hall. At the end of the concert, Dylan returned to the stage to do something he'd never done before and has never done since: read one of his poems in public.

The poem, although not an obituary (Guthrie didn't die until October 1967), is a moving tribute to one of the (maybe the) strongest influences on Dylan's music. What follows is a transcript of Dylan's comments before reading the poem.

There's this book coming out and they asked me to write, uh, something about Woody. Sorta like "What does Woody Guthrie Mean to You" in 25 words. And, uh, I couldn't do it, I wrote out five pages and, uh...I have it here, its a...I have it here by accident, actually. B-but I-I'd like to say this out loud. So, uh...if you could sorta roll along with this thing here, this is called Last Thoughts on Woody Guthrie.

I don't have the words to describe this poem and what it means to me, or how mind-blowingly great it is, like hooking up to a soft-talking, stuttering megawatt line. Eric Clapton had this to say, in an interview with The Telegraph:

He's a poet. Basically he's a poet. He does not trust his voice. He doesn't trust his guitar playing. He doesn't think he's good at anything, except writing—and even then he has self-doubts. Have you heard that thing he wrote about Woody Guthrie? That to me is the sum of his life's work so far. Whatever happens, that is it. That sums it up.


Resources:
Woody Guthrie by icicle
The Voice of Bob Dylan (http://www.procolharum.com/99/rpc_cc_dylan.htm, 10/10/2001)
Liner notes to The Bootleg Series Volumes 1-3 (rare & unreleased) 1961 - 1991.