  Neutron spectroscopic measurements of the magnetic excitations in PrO$_2$
reveal (1) sharp peaks characteristic of transitions between levels of the
$4f^1$ configuration of Pr$^{4+}$ split by the cubic crystal field, and (2)
broad bands of scattering centred near 30 meV and 160 meV. We present a simple
model based on a vibronic Hamiltonian that accounts for the main features of
the data. The analysis shows that $90\pm10$% 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.
