The subthreshold fission cross section of 240Pu was measured relative to the 10B(n,α) or the 6Li(n,α) cross sections from 20 eV to 100 keV. Resonance parameter fits to the data were derived from 20 to 5700 eV. Many more resonances and more resonance structure were observed than in previous measurements. During the course of this measurement, the fission cross sections of 235U and 239Pu were also measured and are compared to the ENDF/B-V evaluation. The 235U experiment is in good agreement with ENDF/B-V; however, the 239Pu measurement is lower than ENDF/B-V and many of the previous measurements, particularly above 25 keV.