The ratio of the neutron capture cross section to the fission cross section, α, for U235 has been measured for incident neutron energies from 3.25 eV to 1.8 keV. A pulsed and collimated neutron beam was passed through a U235 fission chamber placed at the center of a large liquid scintillator, and both capture and fission events in the chamber were detected in the scintillator by means of their prompt gamma rays. A fission event was distinguished from a capture event by a coincidence of the scintillator signal with a signal from the fission chamber. The values of α obtained, after various efficiency and background corrections were applied, are in good agreement with data derived from other experiments.