  We construct two commuting N=2 structures on the space of sections of the
chiral de Rham complex (CDR) of a Calabi-Yau manifold. We use this extra
supersymmetry to construct a non-linear automorphism of CDR preserving these
N=2 structures. Finally, we show how to extend these results to construct a
commuting pair of N=4 super-vertex algebras in the Hyper-Kahler case.
