We propose to develop, build, and fly HaloSat, a CubeSat capable of measuring the oxygen line emission from the hot Galactic halo. A dedicated CubeSat enables an instrument design and observing strategy to maximize the halo signal while minimizing foregrounds from solar wind charge exchange interactions within the solar system. We will use HaloSat to map the distribution of hot gas in the Milky Way and determine whether it fills an extended, and thus massive halo, or whether the halo is compact, and thus does not contribute significantly to the total mass of the Milky Way. HaloSat can be accomplished at modest cost using a CubeSat, a novel platform for space astrophysics missions. We will use a commercially available CubeSat bus and commercially available X-ray detectors to reduce development risk and minimize overall mission cost. HaloSat builds on the initiatives of GSFC/Wallops Flight Facility (WFF) in the development of CubeSats for low cost access to space and relies on the technical expertise of WFF personnel for spacecraft and mission design and operations. The team, from University of Iowa (UI), GSFC, Johns Hopkins, and CNRS (France), contains experts in X-ray detector development and data analysis and the astrophysics of hot plasmas and Galactic structure. The UI team will include a number of junior researchers (undergraduates, graduate students, and a postdoc) and help train them for future leadership roles on NASA space flight missions.