The catalytic abstraction of hydrogen from methane on the (001) surface of Li-doped MgO has been studied at the ab initio level within the periodic unrestricted Hartree-Fock approximation. The catalyst is modeled with an infinite slab, periodic in two dimensions and of finite thickness. Active sites for the reaction are surface O- radical ions resulting from coupling with the Li+ dopants; in the periodic model they are regularly distributed upon the surface. At 0 K the energy difference between reactants and products is close to zero, but a potential barrier of 18 kcal/mol is found to reach the transition state. Relaxation of ions in the zone of the Li+/O- couple stabilizes the reaction products,and plays a fundamental role in the energy balance.