A study of photofission fragment angular distributions on 232Th and 238U has been completed for the first time using linearly-polarized, quasi-monoenergetic photon beams of near-barrier energies. Large polarization asymmetries are observed in both nuclei. For 232Th, fragments are emitted in the direction of beam polarization with more than fifteen times greater preference than perpendicular to it when the beam energy is 6.2 MeV. These asymmetries are roughly a factor of two times greater than are characteristic of 238U. The large observed fragment asymmetries are responsible for asymmetries in the accompanying prompt-fission neutron angular distributions that have recently been measured . A smooth decrease in the polarization asymmetry has also been observed as beam energies increase from 5.9 MeV to 7.6 MeV. The smooth variations reveal no resonant fission processes in the same energy range.  J.M. Mueller et al. Phys. Rev. C 85, 014605 (2012).