  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 the metastable,
high-pressure rocksalt phase (also wide-gap) with Li as an external dopant.
Using modern first-principles defect theory, we predict Li to dope the rocksalt
phase $p$-type by preferentially substituting for Zn and introducing shallow
acceptor levels. Formation of compensating donors like interstitial Li and/or
hydrogen, ubiqutous in the wurtzite phase, is inhibited by the close-packed
nature of the rocksalt structure, which also exhibits relatively high absolute
valence band edge that promotes low hole effective mass and hole
delocalization. Resulting concentrations of free holes are predicted to exceed
$\sim10^{19}$ cm$^{-3}$ under O-rich synthesis conditions while under O-poor
conditions the system remains $n$-type dopable. In addition to revealing
compelling opportunities offered by the metastable rocksalt structure in
realizing a long-sought $p$-type ZnO our results present polymorphism as a
promising route to overcoming strong doping asymmetry of wide-band gap oxides.
