Using (MgO)(4), (MgO)(6), and (MgO)(8) clusters as models of the MgO surface, the structures and energies of H-2 chemisorption on various pair sites are studied with ab initio molecular orbital calculations. The effect of Madelung potential on the chemisorption energetics is also studied. The chemisorption energy is not very sensitive to the cluster size used in the calculation. It however depends strongly on the coordination numbers of Mg and O at the chemisorption site, and decreases in the following order : the valley site much greater than Mg-3c-O-3c much greater than Mg-4c-O-3c > Mg-3c-O-4c site. The valley and the Mg-3c-O-3c pair sites are strongly bonding, whereas the Mg-4c-O-3c and the Mg-3c-O-4c sites are only marginally bonding. All other higher coordination sites are nonbonding. The coordination number of the nearest neighbor atoms only secondarily affects the stability of hydrogen chemisorption. The contribution of electron correlation to the chemisorption energy is essentially determined only by the localized electrons near the chemisorption site.