I found the chords to it in an old book of American folk songs as a different version. So this is how I play it:

Am      Em      F               C
There I sat on Buttermilk Hill
Em         Am             F         C
Who can blame me, cry my fill
       Am    E7             F       Dm
And ev'ry tear would turn a mill,
Am       Em            Am
Johnny's gone for a soldier.