The high-pressure thermodynamic properties of molecular and metallic hydrogen are calculated from the fundamental viewpoint of statistical mechanics. In the molecular solid phase the interaction between hydrogen molecules is taken to be an angle-dependent de Boer repulsion, fitted to the theoretical results of Hirschfelder, Magnasco, Mason, McWeeny, and Musso, with spherical attractions as calculated by Margenau. Thermo dynamic properties for the denser metallic phase are obtained from an improved self consistent version of the Wigner-Huntington calculation, in which the correlations due to electronic repulsions are more closely approximated and in which the Kohn-Sharn local exchange is used. By comparing the Gibbs free energies of the molecular solid and the metal, we predict a phase transition linking the two at 840 kbars, well within the reach of several experiments now being designed.