A porous hybrid inorganic/organic material, NaNi3(OH)(SIP)2 [SIP = 5-sulfoisophthalate][1], is shown to strongly bind molecular hydrogen at coordinatively unsaturated metal sites. A combination of H2 sorption isotherms, temperature programmed desorption, and inelastic neutron scattering spectroscopy show the existence of a considerable number of such strong binding sites in [1] along with other sites where hydrogen is more weakly physisorbed. The overall capacity for hydrogen of this material as well as the much stronger binding of hydrogen than in typical porous material represent an important step toward a possible utilization of porous media for hydrogen storage.