Clean, ordered GaN(0001)-(1 X 1) surfaces are prepared by sputtering with nitrogen ions followed by annealing in ultrahigh vaccum. The surfaces are subsequently exposed at room temperature to O-2 and the chemisorption process studied using Auger, valence and core-level photoemission and electron energy loss spectroscopies, low-energy electron diffraction, and work function measurements. Saturation occurs at a coverage of Theta(ox)=0.4 ML and is accompanied by the removal of surface slates near the band edges. The continued presence of a clear (1 x 1) diffraction pattern, together with other data, indicates a well-defined adsorption site, but the relative importance of Ga-O and N-O bonding remains undetermined. The realization that surface states exist near the valence-band maximum has led to a more accurate determination of the surface Fermi-level pinning position, and of dependent quantities, than given previously. Clean-surface data are also compared with those for surfaces prepared by in situ deposition of Ga metal followed by thermal desorption. No significant differences are seen, which suggests that nitrogen-ion sputtering and annealing is suitable for preparing clean, ordered GaN(0001)-(1 X 1) surfaces. The results for O chemisorption on atomically clean surfaces have been applied to evaluating the passivation of surfaces prepared by ex situ wet-chemical cleaning. The hand bending is found to be similar to 0.5 eV less than on atomically clean surfaces.