We have performed density functional theory calculations on the dissociation of molecular hydrogen on small gas-phase and silica-supported Cu clusters and on the Cu(lll) surface. The Cu surface and the silica support have been represented by cluster models. The supported Cu clusters interact with a nonbridging oxygen, a paramagnetic defect present on the surface of dehydroxylated silica, giving rise to a partial charge transfer to the substrate. While free Cu clusters and the Cu metal are rather unreactive toward H-2 dissociative adsorption, the supported clusters exhibit a much higher reactivity connected with a strong geometrical rearrangement of the metal structure. As a consequence of the interaction with the substrate, the Cu clusters become active catalysts in H-2 dissociation.