The photofission cross-section of 238U was measured at sub-barrier energies as a function of the gamma-ray energy using, for the first time, a monochromatic, high-brilliance, Compton-backscattered gamma-ray beam. The experiment was performed at the High Intensity gamma-ray Source (HIgS) facility at beam energies between E=4.7 MeV and 6.0 MeV and with ~3% energy resolution. Indications of transmission resonances have been observed at gamma-ray beam energies of E=5.1 MeV and 5.6 MeV with moderate amplitudes. The triple-humped fission barrier parameters of 238U have been determined by fitting EMPIRE-3.1 nuclear reaction code calculations to the experimental photofission cross section.