As long-baseline neutrino experiments enter the precision era, the difficulties associated with understanding neutrino interaction cross sections on atomic nuclei are expected to limit experimental sensitivities to oscillation parameters. In particular, the ability to relate experimental observables to neutrino energy in previous experiments has relied solely on theoretical models of neutrino-nucleus interactions, which currently suffer from very large theoretical uncertainties. By observing charged current $ u_mu$ interactions over a continuous range of off-axis angles from 1 to 4 degrees, the nuPRISM water Cherenkov detector can provide a direct measurement of the far detector lepton kinematics for any given set of oscillation parameters, which largely removes neutrino interaction modeling uncertainties from T2K oscillation measurements. This naturally provides a direct constraint on the relationship between lepton kinematics and neutrino energy. In addition, nuPRISM is a sensitive probe of sterile neutrino oscillations with multiple energy spectra, which provides unique constraints on possible background-related explanations of the MiniBooNE anomaly. Finally, high-precision measurements of neutrino cross sections on water are possible, including $ u_e$ measurements and the first ever measurements of neutral current interactions as a function of neutrino energy. The nuPRISM detector also benefits the proposed Hyper-Kamiokande project. A demonstration that neutrino interaction uncertainties can be controlled will be important to understanding the physics reach of Hyper-K. In addition, nuPRISM will provide an easily accessible prototype detector for many of the new hardware components currently under consideration for Hyper-K. The following document presents the configuration, physics impact, and preliminary cost estimates for a nuPRISM detector in the J-PARC neutrino beamline.