We propose the development of a novel muon-proton and muon-nucleus collider facility at the TeV scale that is capable of performing precision deep inelastic scattering measurements in new regimes and providing a rich program in nuclear and particle physics. Such a facility could seed, or leverage, the development of a muon-antimuon collider and make use of the existing hadron accelerator infrastructure when sited at a facility such as Brookhaven National Laboratory, Fermilab, or CERN. We discuss the possible energy and luminosity design parameters for several collider configurations, and illustrate the science potential with several studies on deep inelastic scattering kinematics, Higgs and vector boson production, top quark production, and beyond Standard Model leptoquark production. Detector design considerations and a possible road map toward development are also given.