Neutron spectroscopic measurements of the magnetic excitations in PrO2 reveal (1) sharp peaks characteristic of transitions between levels of the 4f(1) configuration of Pr4+ split by the cubic crystal field, and (2) broad bands of scattering centered near 30 and 160 meV. We present a simple model based on a vibronic Hamiltonian that accounts for these contrasting features of the data. The analysis shows that 90%+/-10% of the Pr ions have a localized 4f(1) configuration and provides strong evidence for a dynamic Jahn-Teller effect in the gamma(8) electronic ground state.