The thermal conductivity of uranium dioxide has been studied for over half a century, as uranium dioxide is the fuel used in a majority of operating nuclear reactors and thermal conductivity controls the conversion of heat produced by fission events to electricity. Because uranium dioxide is a cubic compound and thermal conductivity is a second-rank tensor, it has always been assumed to be isotropic. We report thermal conductivity measurements on oriented uranium dioxide single crystals that show anisotropy from 4 K to above 300 K. Our results indicate that phonon-spin scattering is important for understanding the general thermal conductivity behaviour, and also explains the anisotropy by coupling to the applied temperature gradient and breaking cubic symmetry.