A photofission experiment was performed on targets of 235 U, 238 U, 239 Pu, and 232 Th using nearly 100% linearly polarized, high intensity (∼ 10 7 γ/s), and nearly-monoenergetic γ-ray beams having energies between 5.6 MeV and 7.3 MeV at the High Intensity γ-ray Source (HIγS). An array of 18 liquid scintillator detectors was used to measure prompt fission neutron polarization asymmetries.An asymmetry close to zero was found for 235 U and 239 Pu while a significant asymmetry (∼ 0.5) was found for 238 U and 232 Th. A simplified model of near-threshold photofission has been developed in an attempt to explain the systematic difference between the even-even and even-odd targets. The results of a simulation, based on this model and using previous measurements of fission fragment angular distributions, are shown to accurately reproduce the essential features of the data.