We propose a system that can store molecular hydrogen in densities up to similar to 100 g/L. Our ab initio calculations predict the existence of an oxidized calcium dihydrogen complex, which holds up to eight H(2), i.e., Ca(ion)(H(2))(8). The dihydrogen binding to the Ca is via a weak electron-donation mechanism from the occupied H(2) sigma orbital to the unoccupied, but bound, Ca 3d orbitals. Because of the high concentration of the hydrogen in such complexes, even in calcium-intercalated pillared graphite, one can obtain reversible hydrogen storage denser than that of liquid hydrogen, 70 g/L.