We present a study on the catalytic cycle responsible for coupling of methane by molecular oxygen over a lithium-doped magnesium oxide catalyst. To elucidate the mechanism by which methyl radicals are produced and the active sites are regenerated, geometries and energies of relevant reaction intermediates were determined using an ab initio embedded cluster model. Our results suggest a new mechanism that requires only one active site and does not involve the energetically costly process of creating lattice vacancies. This mechanism is more consistent with the available experimental data than the Ito-Lunsford mechanism proposed earlier.