We explore the physics of crystallization in the deep interiors of white dwarf (WD) stars using the color-magnitude diagram and luminosity function constructed from proper- motion cleaned Hubble Space Telescope photometry of the globular cluster NGC 6397. We demonstrate that the data are consistent with the theory of crystallization of the ions in the interior of WD stars and provide the first empirical evidence that the phase transition is first order: latent heat is released in the process of crystallization as predicted by van Horn. We outline how these data can be used to observationally constrain the value of Gamma = E(Coulomb)/E(thermal) near the onset of crystallization, the central carbon/oxygen abundance, and the importance of phase separation.