The prompt fission neutron spectrum (PFNS) from neutron-induced fission is a fundamental quantity for the behavior of nuclear reactors, and has been measured many times on a wide variety of nuclei and covering different ranges of incident and emitted neutron energies. However, results from past measurements are frequently called into question in modern nuclear data evaluations because of a lack of thorough experimental documentation and incomplete uncertainty analyses. The Chi-Nu experiment at Los Alamos National Laboratory was designed to produce high-precision measurements of the PFNS of major actinides over a wide range of incident and emitted neutron energies, and with the documentation and covariance analysis required to ensure that the results of this experiment maintain their impact long into the future, thereby avoiding this pitfall of past measurements. In this work we describe the Chi-Nu experiment along with summaries of the treatment of and methods developed to address two important components of the analysis of Chi-Nu data: random-coincidence backgrounds and MCNP simulations. Furthermore, we describe the first results for correlations not just between all data points collected on a single target nucleus, but also between all data points from separate Chi-Nu measurements on 235U and 239Pu. These correlations are important for accurately calculating ratios of the PFNS from one actinide to another, which are rare and can be informative for nuclear data evaluation efforts.