As open N = 2 or 4 strings describe self-dual N = 4 Yang-Mills theory in 2 + 2 dimensions, the corresponding closed (heterotic) strings describe self-dual ungauged (gauged) N = 8 supergravity. These theories are conveniently formulated in a chiral superspace with general supercoordinate and local OSp(8\2) gauge invariances. The super-light-cone and covariant-component actions are analyzed. Because only half the Lorentz group is gauged, the gravity field equation is just the vanishing of the torsion.