Here is Crosby, Stills, Nash and Young live at Big Sur, California on September 14, 1969 . . . doing Neil’s Down By The River. This could have been the first public performance of the song. I don’t think they did it at Woodstock. It was recorded January 17, 1969 and released on May 14, 1969.
The Band: Neil Young (vocal, guitar), Stephen Stills (guitar, vocal), David Crosby (guitar, vocal), Graham Nash (keyboards), Greg Reeves (bass), Dallas Taylor (drums).
Graham Nash On How/Why Neil Young Joined Crosby Stills & Nash.
The DVD of Big Sur Celebration only become available a couple years ago.