We extend our statistical mechanical theory of the glass transition from examples consisting of point particles to molecular liquids with internal degrees of freedom. As before, the fundamental assertion is that supercooled liquids are ergodic, although becoming very viscous at lower temperatures, and are therefore describable in principle by statistical mechanics. The theory is based on analyzing the local neighborhoods of each molecule, and a statistical mechanical weight is assigned to every possible local organization. This results in an approximate theory that is in very good agreement with simulations regarding both thermodynamical and dynamical properties.