We have developed a computational approach for predicting protein-protein association rates (Alsallaq and Zhou, Structure 2007, 15, 215). Here we expand the range of applicability of this approach to protein-RNA binding and report the first results for protein-RNA binding rates predicted from atomistic modeling. The system studied is the U1A protein and stem/loop II of the U1 small nuclear RNA. Experimentally it was observed that the binding rate is significantly reduced by increasing salt concentration while the dissociation changes little with salt concentration, and charges distant from the binding site make marginal contribution to the binding rate. These observations are rationalized. Moreover, predicted effects of salt and charge mutations are found to be in quantitative agreement with experimental results.