From a 1967 Ed Sullivan performance. We get to see Brian Jones on recorder, as well as the improbably-young surviving Stones in this one. According to Wikipedia, Keith Richards wrote the song for one of the Stones' groupies in a Los Angeles hotel room in early 1966.
"That's a wonderful song," Mick Jagger told Jann Wenner in 1995. "It's just a nice melody, really. And a lovely lyric. Neither of which I wrote, but I always enjoy singing it." Bill Wyman also notes in his Rolling with the Stones that the song was written by Keith Richards. However, Marianne Faithfull claims that the song was written by Brian Jones, and that Richards only added minor parts to it. Certainly, the recorder is a Jones' signature touch, but at this point in time the authorship is likely to remain unresolved.