The fission cross section of 243Am was measured in the neutron energy range from 1 eV to 10 MeV. Several methods of neutron production were employed using the Van de Graaff accelerator and the electron linear accelerator of the Central Bureau of Nuclear Measurements. The energy averaged fission cross section measured at the Geel electron linear accelerator (GELINA) above 100 eV and the fission cross sections measured at the Van de Graaff above 350 keV were determined relative to the 235U(n,f) cross section. The detailed neutron cross sections measured at GELINA in the 1-eV to 30-keV range were measured relative to the 6Li(n, t)4He cross-section shape and were normalized to the known fission integral of 235U between 7.8 and 11 eV. The present data provide unique new information between 1 and 50 eV. In this energy range, fission areas from 31 resonances were determined. In the subthreshold region above 100 eV, the present results demand drastic corrections of the evaluated data files by factors up to 6. Between the first and second chance fission threshold, the present experiment supports the ZEBRA integral experiment, which suggested a reduction of the fission cross section of 243Am in this region by 12% with respect to an earlier data set.