First recorded by The Everly Brothers (1962, released 1984).
Hit versions by The Cookies (US #17/R&B #7/UK #50 1962), The Beatles (1963).
From the wiki: “‘Chains’ was 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‘). It was first recorded by the Everly Brothers in 1962 but went unreleased until 1984.
“The same year, ‘Chains’ became a US Top 20 hit for Little Eva’s backing singers, The Cookies (with Earl-Jean McRae (‘I’m Into Something Good‘) singing lead), with an arrangement produced by co-writer Goffin.and later covered by The Beatles.
“‘Chains’ became a popular cover song for Liverpool bands after its US release in November 1962. Included briefly in the Beatles’ live sets during their final Cavern gigs before Beatlemania stardom, the group recorded it on February 11, 1963 in four takes (the first proved to be the best) for inclusion on their British debut album, Please Please Me.”
The Cookies, “Chains” (1962):
The Beatles, “Chains” (1963):