The N = 1 self-dual supergravity has SL(2, ℂ symmetry. This symmetry results in SU(2) charges as the angular momentum. As in nonsupersymmetric self-dual gravity, the currents are also of their potentials and are therefore identically conserved. The charges are generally invariant and gauge covariant under local SU(2) transforms and approach being rigid at spatial infinity. The Poisson brackets constitute the su(2) algebra and hence can be interpreted as the generally covariant conservative angular momentum.