She wrote it on guitar.
For those who will demand "PROOF!" watch her on the Chris Isaak show where she says so. (She's said it elsewhere too).She says she learned just a few chords from her guitar teacher and hey it was enough to write songs so why learn more.
https://www.youtube.com/watch?v=-1IzkcW22JA See from about 1:20 on.
She also seems to indicate that her first song, I've Loved and I've Lost was co written with her guitar teacher.... which would not surprise me.