The U(1) Problem in Chiral Random Matrix Models

We show that conventional asymmetric chiral random matrix models (ChRMM), with a gaussian distribution in the asymmetry, provide for a screening of the topological charge and a resolution of the $U(1)$ problem in the unquenched approximation. Our exact results to order $1/N$ are in agreement with numerical estimates using large ensembles of asymmetric ChRMM with gaussian distributions.