Using grand canonical Monte Carlo simulations, we study the crystallization of colloidal hard spheres under gravity. More specifically, we investigate the nature of the freezing transition as a function of gravity and chemical potential of the hard spheres. We find a discontinuous freezing transition where several fluid layers close to the bottom of the sample freeze simultaneously, i.e., at the same chemical potential. We also find that the number of layers that freezes at the same chemical potential decreases for higher gravitational field strength. Upon increasing the chemical potential further, the crystalline film thickness increases continuously.