We report the current results of a large effort to accurately measure the Prompt Fission Neutron Spectra (PFNS) for neutron-induced fission of 235U and 239Pu for incident neutrons with energies from 1 to 20 MeV. The Chi-Nu experiment at the Los Alamos Neutron Science Center used an unmoderated, white spectrum of neutrons to induce fission in actinide samples that were placed inside a parallel plate avalanche counter to provide a fast fission signal. A double time-of-flight technique was used to determine the incoming and outgoing neutron energies. Two neutron detector arrays, one with 54 liquid scintillators and another with 22 lithium glass detectors, were used to detect the outgoing neutrons and measure the PFNS distributions over a wide range in outgoing neutron energy, from below 100 keV to 10 MeV. Extensive Monte Carlo modeling was used to understand the experiment response and extract the PFNS. Systematic errors and uncertainties in the method have been examined and quantified. A summary of these results for incoming energies from 1 to 5 MeV is presented here.