The Lunar Polar Hydrogen Mapper (LunaH-Map) mission will map hydrogen enrichments within permanently shadowed regions at the lunar south pole using a miniature neutron spectrometer. While hydrogen enrichments have been identified regionally from previous orbital missions, the spatial extent of these regions are often below the resolution of the neutron instruments that have flown on lunar missions. LunaH-Map will enter into an elliptical, low altitude perseline orbit which will enable the mission to spatially isolate and constrain the hydrogen enrichments within permanently shadowed regions. LunaH-Map will use a solid iodine ion propulsion system, X-Band radio communications through the NASA Deep Space Network, star tracker, C&DH and EPS systems from Blue Canyon Technologies, solar arrays from MMA Designs, LLC, mission design and navigation by KinetX. Spacecraft systems design, integration, qualification, test and mission operations are performed by Arizona State University