Results of gradient-corrected periodic density functional theory calculations are reported for hydrogen abstraction from methane at O-(s)(2-), O-(s)(-), O-2(s)(2-), point defect, and Sr2+-doped surface sites on La2O3(001). The results show that the anionic O-(s)(-) species is the most active surface oxygen site. The overall reaction energy to activate methane at an O-(s)(-) site to form a surface hydroxyl group and gas-phase .CH3 radical is 8.2 kcal/mol, with an activation barrier of 10.1 kcal/mol. The binding energy of hydrogen at an O-(s)(-) site is - 102 kcal/mol. An oxygen site with similar activity can be generated by doping strontium into the oxide by a direct Sr2+/La3+ exchange at the surface. The O--like nature of the surface site is reflected in a calculated hydrogen binding energy of -109.7 kcal/mol. Calculations indicate that surface peroxide (O-2(s)(2-)) sites can be generated by adsorption of O-2 at surface oxygen vacancies, as well as by dissociative adsorption of O-2 across the closed-shell oxide surface of La2O3(001). The overall reaction energy and apparent activation barrier for the latter pathway are calculated to be only 12.1 and 33.0 kcal/mol, respectively. Irrespective of the route to peroxide formation, the O-2(s)(2-) intermediate is characterized by a bent orientation with respect to the surface and an O-O bond length of 1.47 Angstrom; both attributes are consistent with structural features characteristic of classical peroxides. We found surface peroxide sites to be slightly less favorable for H-abstraction from methane than the O-(s)(-) species, with DeltaE(rxn)(CH4) = 39.3 kcal/mol, E-act = 47.3 kcal/mol, and DeltaE(ads)(H) = -71.5 kcal/mol. A possible mechanism for oxidative coupling of methane over La2O3(001) involving surface peroxides as the active oxygen source is suggested.