We prove a spontaneous magnetization of the oxygen-terminated ZnO (0001) surface by utilizing a multicode, SIESTA and KKR, first-principles approach, involving both LSDA+U and self-interaction corrections to treat electron correlation effects. Critical temperatures are estimated from Monte Carlo simulations, showing that at and above 300 K the surface is thermodynamically stable and ferromagnetic. The observed half-metallicity and long-rage magnetic order originate from the presence of p holes in the valence band of the oxide. The mechanism is universal in ionic oxides and points to a new route for the design of ferromagnetic low-dimensional systems.