Watch: Taylor Swift and the Rolling Stones perform "As Tears Go By" Taylor Swift got a taste of some classic rock and roll this week. The country/pop darling joined none other than The Rolling Stones onstage during the band's stop in Chicago on Monday. And the Rolling Stones just unveiled a video of it. Swift hit the stage during the Stones' performance of the 1965 song, "As Tears Gone By," written by Mick Jagger and Keith Richards. It was also a hit for Marianne Faithful -- so perhaps the Stones though Swift be a good fit to take it on in concert. After the appearance Swift said backstage, "You know that's not something I thought was going to happen in my life!" Swift isn't first star to pop up at the Stones' "50 and Counting" tour. Other guests have included Lady Gaga, Katy Perry, Tom Waits and Dave Grohl.