  An unusual four-dimensional generally covariant and supersymmetric SU(2)
gauge theory is described. The theory has propagating degrees of freedom, and
is invariant under a local (left-handed) chiral supersymmetry, which is half
the supersymmetry of supergravity. The Hamiltonian 3+1 decomposition of the
theory reveals the remarkable feature that the local supersymmetry is a
consequence of Yang-Mills symmetry, in a manner reminiscent of how general
coordinate invariance in Chern-Simons theory is a consequence of Yang-Mills
symmetry. It is possible to write down an infinite number of conserved
currents, which strongly suggests that the theory is classically integrable. A
possible scheme for non-perturbative quantization is outlined. This utilizes
ideas that have been developed and applied recently to the problem of
quantizing gravity.
