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A map of surface molecular water was derived from long slit spectroscopy of the south polar region of the Moon using the Faint Object infraRed CAmera for the SOFIA Telescope spectrometer on the Stratospheric Observatory for Infrared Astronomy. Mean water abundances detected are about 250 μg/g over that of a mare reference surface at Mare Fecunditatis. Water abundances are locally anticorrelated with temperature. The distribution of water is consistent with derivation of water from pre‐existing hydroxyl subsequently trapped in impact glass, provided hydroxyl increases with latitude as some models and measurements suggest. The detected water cannot be in equilibrium with the exosphere because insufficient water is present in the exosphere to maintain the surface abundance. The data are consistent with a high latitude water‐bearing mineral host that may be a precursor to recently detected high latitude hematite. Plain Language Summary: If water is present in sufficient quantities on the Moon, it may be an important resource for space exploration as it can be used to make rocket fuel and sustain human presence. Water molecules on the illuminated surface of the Moon can be detected using a unique spectral signature that is obscured from telescopes on Earth's surface by water vapor in the atmosphere. The NASA/DLR Stratospheric Observatory for Infrared Astronomy is a large telescope on a 747 aircraft that operates high in the stratosphere above 99% of the water vapor, and so can detect the infrared thermal emission from water on the Moon's surface. Near the South Pole, we produced a map of water emission that shows water is present at a few hundred parts per million, and is inversely correlated with surface temperature. This is consistent both with the behavior of water free to migrate on the surface, and water bound up in glass from meteorite impacts. However, the amount of water we find probably cannot be freely exchanging with the Moon's tenuous exosphere because it would require much more water in the exosphere than has been measured. Key Points: Stratospheric Observatory for Infrared Astronomy + Faint Object infraRed CAmera for the SOFIA Telescope confirms the presence of water emission in the South Polar Region of the MoonSmall maps of water emission are presented that begin to enable tests of various hypotheses for water formation and variationObservations suggest the water cannot migrate and instead is trapped within impact glasses or in a mineral‐based host [ABSTRACT FROM AUTHOR]