GJ 1132b is a nearby Earth-sized exoplanet transiting an M dwarf, and is among the most highly characterizable small exoplanets currently known. In this paper, we study the interaction of a magma ocean with a water-rich atmosphere on GJ 1132b and determine that it must have begun with more than 5 wt% initial water in order to still retain a water-based atmosphere. We also determine the amount of O[subscript 2] that can build up in the atmosphere as a result of hydrogen dissociation and loss. We find that the magma ocean absorbs at most ~10% of the O[subscript 2] produced, whereas more than 90% is lost to space through hydrodynamic drag. The most common outcome for GJ 1132b from our simulations is a tenuous atmosphere dominated by O[subscript 2], though, for very large initial water abundances, atmospheres with several thousands of bars of O[subscript 2] are possible. A substantial steam envelope would indicate either the existence of an earlier H[subscript 2] envelope or low XUV flux over the system's lifetime. A steam atmosphere would also imply the continued existence of a magma ocean on GJ 1132b. Further modeling is needed to study the evolution of CO[subscript 2] or N[subscript 2]-rich atmospheres on GJ 1132b.MIT Torres Fellowship for Exoplanet Research