I'll explain a new way of looking at 4d supergravity --- as a theory of holomorphic maps into Penrose's twistor space. Allowing twistor space to have N fermionic directions, the theory is anomaly free when N=8. Via the Penrose transform, the vertex operators correspond to an N=8 Einstein supergravity multiplet. Conformal symmetry is explicitly broken by the presence of the infinity twistor in the BRST operator. I will show how to compute the complete classical S-matrix from worldsheet correlation functions, and interpret these amplitudes geometrically.