A model of solvation, including both explicit water molecules and a description of the remaining solvent, based upon the polarizable continuum model is described and used to study the acceleration of the Claisen rearrangement of allyl vinyl ether observed in aqueous medium. The calculations, at the ab initio HF/6-31G* and MP2 levels, show that the major effect of the solvent is effectively modelled by the explicit water molecules. This model yields a barrier lowering in excellent agreement with experiment. The changes in the kinetic isotope effects arising from hydration, predicted by our treatment, differ somewhat from those suggested by experiment.