Consistent Supergravity with Complex Spin-32Gauge Fields

We construct a new theory of supergravity which is invariant under complex local supersymmetry transformations. This theory is obtained by coupling the massless spin-($\frac{3}{2},1$) multiplet of ordinary global supersymmetry to the spin-($2,\frac{3}{2}$) gauge multiplet of previous supergravity.