The chemisorption of molecules on metal oxide surfaces is generally considered to occur by either an acid/base or a redox mechanism, with the former dominating on nonreducible and insulating oxides such as MgO. NO, NO2, and the less familiar NO3 are atypical adsorbates in that their most,potent Lewis acidic and basic forms are generated by one-electron oxidation or reduction of the parent molecules. In this work, first-principles density functional theory supercell calculations are used to probe the adsorption chemistry of the nitrogen oxides on an undefected MgO(001) surface. The isolated adsorbates are found to physisorb (NO, NO2) or weakly chemisorb (NO3) to the MgO terrace. In contrast, adsorbate partners located on neighboring surface acid (Mg-s) and base (O-s) sites form strongly chemisorbed products with features characteristic of nitrite (NO2-) and nitrate (NO3-). The origin of this new class of "cooperative" chemisorption is shown to be electron transfer between two NOx species to generate Lewis acid (NOx+) and base (NOx-) pairs that strongly chemisorb to the MgO surface and that are further stabilized by lateral electrostatic attraction. The relatively low ionization potentials and large electron affinities of the NOx molecules are key to enabling the cooperative effect on MgO. Even more pronounced cooperative effects are expected for NOx adsorption on more basic or acidic oxides, including those used for NOx remediation. The effect is also likely to have a role in the heterogeneous chemistry of other odd-electron adsorbates, including the halogen oxides and HOx radicals.