The solid-liquid equilibrium of hard dumbbells with embedded point dipoles is calculated using a generalized van der Waals theory to account for long range attractive forces. Molecular parameters are chosen to model a methyl chloride molecule. The solid free energy is calculated using the cell theory of Lennard-Jones and Devonshire with the dipolar contribution estimated by static lattice sums. Thermodynamic perturbation theory is used to add dipolar effects to a hard dumbbell fluid equation of state. The resulting phase equilibria show that the dipole does have a significant effect in determining the stable solid structure on freezing. In particular, the dipole moment stabilizes a non-close-packed orthorhombic structure, similar to the known solid structure of methyl chloride. An increase in the ratio of triple point temperature to critical point temperature is also observed as the dipole moment is increased, as is a decrease in the density change on freezing. At high pressure and temperature a solid-solid-liquid triple point is found, above which the system freezes into the close-packed structure.