Nuclear fission is a decay process where a nucleus divides into two fragments, releasing large amounts of energy and emitting prompt neutrons. There is significant interest in methods to distinguish fissile material (material which can undergo a chain fission reaction, where those prompt neutrons induce more fission events) from non-fissile material. A novel method to distinguish fissile from non-fissile material has been developed at the High Intensity Gamma-ray Source (HIGS) at Duke. A photofission experiment was performed on 235,238U, 239Pu, and 232Th using nearly 100% linearly polarized γ-ray beams of energies between 5.6 and 7.3 MeV at HIGS. An array of 18 liquid scintillating detectors was used to measure prompt fission neutron angular distributions. The ratios of prompt fission neutron yields parallel to the plane of beam polarization to the yields perpendicular to this plane were measured as a function of beam and neutron energy. A ratio near unity was found for 235U and 239Pu while a significant ratio (~3) was found for 238U and 232Th. This significant difference could potentially be used to distinguish fissile isotopes (such as 235U and 239Pu) from non-fissile isotopes (such as 238U and 232Th). A simulation, based on a simplified model of fission and using previous measurements of fission fragment angular distributions, is able to account for our experimental values of prompt neutron polarization ratios.