We report an application of diffusion Monte Carlo to investigate the importance of three-body forces on the properties of the water trimer. The potential energy surface used is due to Millot and Stone and is based on intermolecular perturbation theory to which three-body induction and dispersion energies are added. The effects of the three-body forces are considered by comparison with the same potential containing only pairwise water interactions. We have calculated minimum energy structures, vibrationally averaged structures, zero-point energies, rotational constants, cluster dissociation energies, and tunneling splittings, with and without the three-body forces. The values obtained for the vibrationally averaged rotational constants with the three-body potential are fairly close to the experimental values. Whereas the rotational constants are shown to have a significant dependence, the tunneling splittings are changed little by the three-body forces. Based on the calculated difference in anharmonic zero-point energies in water dimer and trimer, we predict that vibrational excitation of a stretching mode will cause predissociation in (H2O)(3) but probably not in (D2O)(3).