A high-conductivity two-dimensional (2D) hole gas, analogous to the ubiquitous 2D electron gas, is desirable in nitride semiconductors for wide-bandgap p-channel transistors. We report the observation of a polarization-induced high-density 2D hole gas in epitaxially grown gallium nitride on aluminium nitride and show that such hole gases can form without acceptor dopants.The measured high 2D hole gas densities of about 5 x 10(13) per square centimeters remain unchanged down to cryogenic temperatures and allow some of the lowest p-type sheet resistances among all wide-bandgap semiconductors. The observed results provide a probe for studying the valence band structure and transport properties of wide-bandgap nitride interfaces.