We report that calculating the Gibbs free energy of the alpha-Al2O3 (0001) surfaces in equilibrium with a realistic environment containing both oxygen and hydrogen species is essential for obtaining theoretical predictions consistent with experimental observations. Using density-functional theory we find that even under conditions of high oxygen partial pressure the metal-terminated surface is surprisingly stable. An oxygen-terminated alpha-Al2O3 (0001) surface becomes stable only if hydrogen is present on the surface. In addition, including hydrogen on the surface resolves discrepancies between previous theoretical work and experimental results with respect to the magnitude and direction of surface relaxations.