Two types of divacancy at the (001) surface of MgO are theoretically studied and compared with the corresponding defect in the bulk: the pit, where a surface magnesium and the oxygen ion underneath are removed, and the rub, where both removed ions are at the surface. All calculations have been performed by means of the EMBED program which adopts an embedded-cluster approach in the frame of the Hartree-Fock (HF) approximation [C. Pisani F. Cora, R. Nada, and R. Orlando, Comput. Phys. Commun. 82, 139 (1994); C. Pisani and U. Birkenheuer, ibid. 96, 152 (1996)]; the semi-infinite host crystal for the study of the surface defects has been simulated with a four-layer slab. The energy released on formation of the divacancy from the two charged isolated vacancies is very high, almost 300 kcal/mol. The tub divacancy is the most stable, both as a neutral and as a singly charged defect. For the paramagnetic center tone electron trapped in the cavity), spin density data are provided and discussed with reference to results from electron paramagnetic resonance experiments and molecular cluster calculations [E. Giamello M. C. Paganini, D. Murphy, A. M. Ferrari, and G. Pacchioni, J. Phys. Chem. 101, 971 (1997)]. It is suggested that the tub divacancy is a common defect, if not the most common, at the highly dehydrated MgO surface.