We present the first ab initio density functional theory study of the oxygen-terminated Cr2O3 (0001) surface within the local spin-density approximation (LSDA). We find that spin plays a critical role for even the most basic properties of Cr2O3 such as the structure and mechanical response of the bulk material. The surface exhibits strong relaxations and changes in electronic and magnetic structure with important implications for the chemical reactivity and unusual spin-dependent catalytic activity of the surface. Unlike the bulk, the outermost chromium bilayer is ferromagnetically ordered, and the surface oxygen layer exhibits appreciable net spin polarization in the opposite sense. Surprisingly, despite this ferrimagnetic order, the chemically important states near the Fermi level exhibit ferromagnetic order and thus favor electronic spin alignment of species interacting with the surface. Finally, we also find a high density of unoccupied electronic surface states available to participate in the chemical reactivity of the surface.