  We combine Stein's method with a version of Malliavin calculus on the Poisson
space. As a result, we obtain explicit Berry-Ess\'een bounds in Central Limit
Theorems (CLTs) involving multiple Wiener-It\^o integrals with respect to a
general Poisson measure. We provide several applications to CLTs related to
Ornstein-Uhlenbeck L\'evy processes.
