We present an accurate new method to compute absolute free energies of molecular solids by computer simulations. As a first application, we computed the thermodynamicphase transition between the fluid phase and the orientational disordered solid β phase of nitrogen at 300 K, using a well tested pair potential. The computed coexistence pressure and the volume change coincides within the error margins with the experimental values. The coexistence volume differed by 2% from the experimental value. To our knowledge these results constitutes the first numerical calculation of the thermodynamic stability for a model of a realistic molecular solid.