The adsorption and decomposition of an N2O molecule at different sites on a CaO(s) surface are investigated by means of ab initio quantum chemistry. The calcium, Ca2+, and oxygen, O(s)2-, sites at a perfect (100) surface and at a corner position, O(c)2-, are considered. Adsorption energies at different sites are calculated and the largest value, 6 kcal/mol, is obtained for a corner site. The barrier for dissociation is calculated to 26 and 27 kcal/mol at the O(c)2- and O(s)2- sites, respectively. These values are some 10 kcal/mol lower than the experimental estimate, and the discrepancy is understood from methodological difficulties to describe the free N2O molecule. A mechanism for the dissociation over an O2- site is proposed, whereby the transfer of the O atom goes via a linear N-N...O...O2- transition state.