An extension of Wertheim's first order perturbation theory [M. S. Wertheim, J. Chem. Phys. 87, 7323 (1987)] for chain molecules in the solid phase is proposed. In particular the solid phase of a model of freely jointed chains of tangent hard spheres has been considered. The equation of state and free energies from theory are compared with simulation results obtained previously by Malanoski and Monson [A. P. Malanoski and P. A. Monson, J. Chem. Phys. 107, 6899 (1997)]or chains with up to eight monomer units. The agreement between theory and simulation is good for the densities close to the melting, and deteriorates for densities close to close-packing. We also evaluated theoretically the fluid-solid equilibrium of the pearl-necklace model and compare with simulation results. The theory reproduces reasonably well the trends observed in the simulation results.