First recorded by The Everly Brothers (1962, released 1984).
Hit versions by The Cookies (US #17/R&B #7 1962), The Beatles (1963).
From the wiki: “‘Chains’ is a song composed by the Brill Building husband-and-wife songwriting team Gerry Goffin and Carole King (‘Up on the Roof‘, ‘Crying in the Rain‘, ‘Oh No Not My Baby‘), and originally recorded by the Everly Brothers but which went unreleased until 1984. In 1962 it was a US Top 20 hit for Little Eva’s backing singers, The Cookies, and later covered by The Beatles.
“The single by The Cookies (with Earl-Jean McRae (‘I’m Into Something Good‘) singing lead) was a popular cover song for Liverpool bands after its release in November 1962, and was included briefly in the Beatles’ live sets. They recorded it on February 11, 1963 in four takes (the first proved to be the best) for inclusion on their British debut, Please Please Me.”
The Cookies, “Chains” (1962):
The Beatles, “Chains” (1963):