On the basis of embedded cluster calculations, we propose a new model for the structure of paramagnetic color centers at the MgO surface usually denoted as Fs(H)(+) (an electron trapped near an adsorbed proton). These centers are produced by exposing the surface of polycrystalline MgO to H-2 followed by UV irradiation. We demonstrate that properties of H atom absorbed at surface sites such as step edges (MgOstep) and reverse corner sites (MgORC), formed at the intersection of two step edges, are compatible with a number of features observed for Fs(H)(+). Our calculations suggest that (i) H-2 dissociates at the reverse corner site heterolytically and that there is no barrier for this exothermic reaction; (H) the calculated vibrations of the resulting MgORC(H+)(H-) complex are fully consistent with the measured ones; (iii) desorption of a neutral H atom from the diamagnetic precursor requires UV light and leads to the formation of stable neutral paramagnetic centers at the surface, MgOstep(H+)(e(-))(trapped) and MgORC(H+)(e(-))(trapped). The computed isotropic hyperfine coupling constants and optical transitions of these centers are in broad agreement with the existing experimental data. We argue that these centers, which do not belong to the class of "oxygen vacancies" are two of the many possible forms of the Fs(H)(+) defect center.