That's funny, I just saw the stage version of Grease the other day and one of the songs in the play, Those Magic Changes, is the same chord progression as In The Still of the Night. In the scene, Doody is just learning to play guitar and his buddies put him on the spot to play a tune. He starts the song, fumbling around and singing to himself,
"C, C, C, A minor, F, F, F, G7," and so on, when he finally gets the hang of it, and starts in on the actual lyrics, the T-birds take that over singing the names of the chords and it becomes the background, in place of a doo-wop.
You won't see that in the movie, that's one of the stage songs that gets relegated to background music during the school dance.