  We construct a sheaf of N=2 vertex algebras naturally associated to any
Poisson manifold. The relation of this sheaf to the chiral de Rham complex is
discussed. We reprove the result about the existence of two commuting N = 2
superconformal structures on the space of sections of the chiral de Rham
complex of a Calabi-Yau manifold, but now calculated in a manifest N=2
formalism. We discuss how the semi-classical limit of this sheaf of N=2 vertex
algebras is related to the classical supersymmetric non-linear sigma model.
