We report neutron diffraction data on single crystal PrO2 which reveal a cooperative Jahn-Teller distortion at TD=120±2 K. Below this temperature an internal distortion of the oxygen sublattice causes the unit cell of the crystallographic structure to become doubled along one crystal axis. We discuss several possible models for this structure. The antiferromagnetic structure below TN=13.5 K is found to consist of two components, one of which shares the same doubled unit cell as the distorted crystallographic structure. We also present measurements of the magnetic susceptibility, the specific heat capacity, and the electrical conductivity of PrO2. The susceptibility data show an anomaly at a temperature close to TD. From the specific heat capacity data we deduce that the ground state is doubly degenerate, consistent with a distortion of the cubic local symmetry. We discuss possible mechanisms for this. The conductivity shows an activated behavior with an activation energy Ea=0.262±0.003 eV.