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It is known that covalent semiconductors become superconducting if conveniently doped with large concentration of impurities. In this article we investigate, using ab initio methods, if the same situation is possible for an ionic, large-band gap semiconductor such as ZnO. We concentrate on the cage-like sodalite phase, with very similar electronic and phononic properties as wurtzite ZnO, but allow for endohedral doping of the cages. We find that sodalite ZnO becomes superconducting for a variety of dopants, reaching a maximum critical temperature of 7 K. This value is comparable to the transition temperatures of doped silicon clathrates, cubic silicon, and diamond.