Little is known about dislocation core structures in oxides, despite their central importance in controlling electrical, optical, and mechanical properties. It has often been assumed, on the basis of charge considerations, that a nonstoichiometric core structure could not exist. We report atomic-resolution images that directly resolve the cation and anion sublattices in alumina (alpha-Al2O3). A dissociated basal edge dislocation is seen to consist of two cores; an aluminum column terminates one partial, and an oxygen column terminates the second partial. Each partial core is locally nonstoichiometric due to the excess of aluminum or oxygen at the core. The implication for mechanical properties is that the mobile high-temperature dislocation core structure consists of two closely spaced partial dislocations. For basal slip to occur, synchronized motion of the partials on adjacent planes is required.