I found this from an old, 1998, thread about two-chord songs:

There was a scout camp parody we used to do that requires only one chord:

Dirty Lil, Dirty Lil,
Lives on top of Garbage Hill.
Never washes, never will,
(Hochh, ptoo!) Dirty Lil.

Melody is - in the key of C:
EGG EGG
EGGAEDC
EGGAEGG
(hack, spit) EDC