Prompt fission neutron spectra from $^{239}$Pu($n,f$) were measured for incident neutron energies from $0.7$ to $700,$MeV at the Weapons Neutron Research facility (WNR) of the Los Alamos Neutron Science Center. A newly designed high-efficiency fission chamber was coupled to the highly segmented Chi-Nu array to detect neutrons emitted in fission events. The double time-of-flight technique was used to deduce the incident-neutron energies from the spallation target and the outgoing-neutron energies from the fission chamber. Prompt fission neutron spectra (PFNS) were measured with respect to $^{252}$Cf spontaneous fission down to $200,$keV and up to about $12,$MeV for all the incident neutron energies with typical uncertainties well below $2%$ up to about $10,$MeV outgoing-neutron energy. The general trend of PFNS is well reproduced by JEFF3.3 and ENDF-BVIII.0 evaluations. Discrepancies were however observed for the low-energy part of the spectra, where evaluations overestimate the number of emitted neutrons. Neutron multiplicities and average kinetic energies as a function of incident-neutron energy are obtained experimentally with reported uncertainties below $0.4%$. Neutron multiplicities disagree with some older datasets above $6,$ MeV, indicating the need of using a high-efficiency fission detector, which does not bias the data. The measured mean kinetic energies agree with the most recent data. Evaluations fairly reproduce the trend, but fail to reproduce the experimental values within their uncertainties.
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