Dear JakubThe writer's credit on Midnight Moonlight is listed as Peter Rowan. You can find chords for this at the following URL:
www.rukind.com/music/gdtunes.htm
(This is actually a site primarily dedicated to Grateful Dead lyrics, but you'll find other traditional and not-so-traditional tunes performed by "Old and In the Way" - a collaboration among Jerry Garcia, David Grisman, Peter Rowan, John Kahn and Vassar Clemens in about 1974 - here, too.)
Enjoy!