For High on a hill the simplified chords are:
Bb    Eb   F       X4

Chorus
F    Bb   Gm(?)
F    Bb
Eb    Bb   F       X2
Bb (round, round)

in the Key of C:
Bb=C
Eb=F
F=G
Gm=Am

These are simplified and I'm in no way good at this but they sound fairly right to me. Now I need to get my hands on a banjo.