This was composed by Jerry Leiber and Mike Stoller, who wrote Elvis’s Hound Dog, Jailhouse Rock and Loving You, and co-wrote Stand by Me with Ben E King. It was first released by The Drifters in 1956.
In 1962 a much better version (in my opinion) was released by Dion, who had split from his first vocal group, the Belmonts, and his second, the Del-Satins. It reached No 2 in the US Hot 100 in early 1963 but did nothing in Britain. I don’t understand why.