Chemical reactions involving nitric oxide molecules and a calcium oxide surface are addressed by means of quantum chemistry. The regularised complete active space self-consistent field method (reg-CASSCF) is employed to determine structures and vibrational frequency bands of the monomeric and dimeric surface species. Stabilities are computed by the CASPT2 method. Reactivity trends for the adsorbates are estimated for various surface sites, including bonding to the Ca and O surface atoms, to an oxygen vacancy and to two different edge sites. Implications of excess surface electrons to heterogeneous NO reduction processes at oxide catalysts are discussed.