  Using the Atiyah class we give a criterion for a vector bundle on a
coisotropic subvariety, $Y$, of an algebraic Poisson variety $X$ to admit a
first and second order noncommutative deformation. We also show noncommutative
deformations of a vector bundle are governed by a curved dg Lie algebra which
reduces to the classical relative Hochschild complex when the Poisson structure
on $X$ is trivial.
