LunaH-Map is a new type of NASA planetary science mission. LunaH-Map is a miniaturized, fully functional interplanetary spacecraft the size of a shoebox that will map hydrogen enrichments within permanently shadowed regions of the lunar south pole. The spacecraft will use a miniaturized propulsion system, attitude control, power and communications systems to maneuver into orbit around the Moon. LunaH-Map will enter a low altitude, elliptical polar orbit and will measure the abundance of hydrogen using a new type of compact neutron spectrometer. Neutron measurements made at low altitude over the lunar south pole will allow LunaH-Map to constrain the hydrogen within permanently shadowed regions at unprecedented spatial resolution.