Julee Cruise hit it big around the same time Twin Peaks debuted on ABC. Her 1989 album Floating Into The Night contained a handful of songs used on the show (including the theme) all with lyrics from David Lynch and music by Angelo Badalamenti.
I loved the album and listened to it regularly, long after Twin Peaks was cancelled.
Here's Julie (looking alarmingly like Lady Gaga) on a 1989 BBC-2 television program, performing "Rockin' Back Inside My Heart".