This was written by Paul McCartney while the group were in Hamburg in early 1962 but credited as always to Lennon-McCartney. It was recorded on September 11, 1962, at Abbey Road Studios and released on October 5 as the B-side of their first single under their own name, Love Me Do. This got to No 17 in Britain, and when it was released in America in 1964 it topped their charts. I think this is a better song than Love Me Do. It featured on their 1963 debut album Please Please Me, which I played until it was nearly transparent.
The group played it live on their 1963 BBC radio show Pop Go The Beatles.