Atomistic computer simulation techniques are used to model the surface structures and surface defects of La2O3, an active catalyst for the oxidative coupling of methane. The simulation approach is based upon energy minimization methods and includes the important effect of surface relaxation. The structure of the surface is, therefore, not considered simply as a termination of the bulk lattice. The calculations predict that the {001} and {011} surfaces would dominate the equilibrium crystal morphology, which is consistent with the available electron microscopy data. The formation of O- and O-2(2-) peroxide species, which are believed to be responsible for methane activation, are examined in some detail. Various pair configurations for O--O- are considered both in the bulk and at the surface. Finally, we calculate the energetics of the gas-solid reaction to create such oxygen hole centers which involves the incorporation of molecular O-2 into the lattice at oxygen vacancy sites.