While there are several n-type transparent semiconductor oxides (TSO) for optoelectronic applications (e.g. LEDs, solar cells or display TFTs), their required p-type counterpart oxides are known to be more challenging. At this time, the n-type TSO with the largest bandgap (∼5 eV) is GaO that holds the promise of extending the light transparency further into the deep ultraviolet. In this work, it is demonstrated that strongly compensated GaO is also an intrinsic (or native) p-type TSO with the largest bandgap for any reported p-type TSO (e.g. NiO, SnO, delafossites, oxychalcogenides). The achievement of hole mobility in excess of 10 cm V s and (high temperature) free hole concentrations in the ∼10 cm range challenges the current thinking about achieving p-type conductivity in GaO being "out of the question". The results presented in this paper therefore further clarify that p-type GaO is possible, although more research must be conducted to determine what are the real prospects for GaO solar blind bipolar optoelectronics and ultra-high power electronics based on p-n homojunctions.