In this Letter, we report a new spin ice--Pr2Sn2O7--which appears to have enhanced residual entropy due to the dynamic nature of the spins. Neutron scattering experiments show that at 200 mK, there is a significant amount of magnetic diffuse scattering which can be fit to the dipolar spin-ice model. However, these short-ranged ordered spins have a quasielastic response that is atypical of the canonical spin ices, and suggests that the ground state is dynamic (i.e., composed of locally ordered two-in-two-out spin configurations that can tunnel between energetically equivalent orientations). We report this as an example of a dynamic spin ice down to 200 mK.