This was written by Burt Bacharach, Mack David (Hal's older brother), and Barney Williams (a pen name of Luther Dixon). It was originally "I'll Cherish You," but was re-written at the request of Dixon, who produced the track.
The Shirelles' vocals were added directly to Bacharach's demo recording.
This was a #5 hit for the group Smith in 1969. Smith, fronted by Gayle McCormick, was managed and produced by Del Shannon, who had a #1 hit with "Runaway." Shannon chose the song for the group to record even though none of the members had ever heard of it before. (thanks, Brad Wind - Miami, FL, for all above)
The Beatles recorded this on their first album, Please Please Me. The Beatles also covered "Boys" on this, which was previously performed by The Shirelles. (thanks, Bertrand - Paris, France)