  Self-dual gravity may be reformulated as the two dimensional principal chiral
model with the group of area preserving diffeomorphisms as its gauge group.
Using this formulation, it is shown that self-dual gravity contains an infinite
dimensional hidden symmetry whose generators form the Affine (Kac-Moody)
algebra associated with the Lie algebra of area preserving diffeomorphisms.
This result provides an observable algebra and a solution generating technique
for self-dual gravity.
