We argue that for granular metals a sizable fraction of the grains becomes charged because the energy fluctuation of the highest-occupied level of each grain, as predicted by random matrix theory, is larger than the charging energy. We have computed the ground state density of states and the degree of ionization of granular metals. The density of states shows a Coulomb gap around the Fermi energy, produced by the long-range part of the Coulomb interactions, which should dominate transport properties at low temperatures