This old chestnut of a tune is played in 12/8, so the barline don't correspond. The melody is played over a I-vi-IV-V progression in the key of C, which is one of the most common progression used in fifties slow rock and doo-wop tunes. If you look at the notes used in the melody and relate them to the chords underneath, you can see why it works so well and is such a memorable tune.