This was written by Boudleaux Bryant. The Everly Brothers recorded it in just two takes on March 6, 1958, with Chet Atkins on guitar, and it was released the following month. It topped the charts in the US and Britain.
Here is a live performance from 1960.
A version by Cliff Richard and Phil Everly reached No 14 in Britain in 1994.
Here they sing it live. I think this may be the performance on the single.