Muddy Waters was long one of the Rolling Stones' idols, and they got to perform with him 1981 in Chicago. "Muddy Waters and the Rolling Stones: Live at the Checkerboard Lounge 1981" shows those two sharing the stage with Buddy Guy, Junior Wells, and a bunch of other blues singers.
It starts off with the great Muddy Waters and Little Walter doing their standard repertoire when the Rolling Stones come into the club from a drunken night out. Muddy sees them enter (it is a small compact club) and as they get their drinks in, Muddy calls them to the stage one at a time, orders underlings to fetch some guitars for a jam.