Despite decades of efforts, achieving p-type conductivity in the wide band gap ZnO in its ground-state wurtzite structure continues to be a challenge. Here we detail how p-type ZnO can be realized in a known metastable, high-pressure rocksalt phase (also wide-gap) with Li as an external dopant. Using modern defect theory, we predict Li to dope the rocksalt phase p-type by preferentially substituting for Zn and introducing shallow acceptor levels, resulting in predicted hole concentrations to exceed 1019cm-3. Formation of compensating donors like interstitial Li and unintentional hydrogen, ubiquitous in wurtzite phase, is inhibited by the close-packed nature of the rocksalt polymorph. Also, relatively high absolute valence band edge of rocksalt ZnO benefits low hole effective masses and hole delocalization. In addition to the technological significance, our results reveal polymorphism as a promising route to overcome strong doping asymmetry of wide band gap oxides. © 2018 American Physical Society.