  We prove that homogenous sums inside a fixed discrete Poisson chaos are
universal with respect to normal approximations. This result parallels some
recent findings, in a Gaussian context, by Nourdin, Peccati and Reinert (2010).
As a by-product of our analysis, we provide some refinements of the CLTs for
random variables on the Poisson space proved by Peccati, Sol\'e, Taqqu and
Utzet (2010), and by Peccati and Zheng (2010).
