The fission cross sections of 244Cm, 246Cm, and 248Cm have been measured from 0.1 eV to 80 keV using the Rensselaer Intense Neutron Spectrometer. The cross sections were normalized to the 235U ENDF/B-V broad-bin-averaged fission cross section. Fission areas and widths were determined for the resolved low-energy resonances. In general, the ENDF/B-V fission cross sections for the curium isotopes are in poor agreement with the measured cross sections and a new evaluation of these curium cross sections is recommended. The observation of structure in the measured cross sections in the unresolved region is suggestive of intermediate structure in the even curium isotopes.