Using the density-functional theory within the generalized gradient approximation, we have studied the partial oxidation of methanol on a Cu(111) surface covered with a chemisorbed oxygen layer that resembles a Cu2O layer. Adsorption energies and geometries were computed for methanol, methoxy, hydroxymethyl and formaldehyde on both clean Cu(111) and Cu2O/Cu(111) and electronic structures were computed for the reaction intermediates on Cu2O/Cu(111). We also calculated the energy barrier for partial oxidation of methanol to formaldehyde on Cu2O/Cu(111). These results show that the Cu2O monolayer slightly lowers the stability of each of the surface adsorbates and the oxygen strongly promotes hydrogen dissociation by lowering the energy barrier of methanol decomposition and causing the spontaneous dissociation of methanol into methoxy.