Wertheim's first order thermodynamic perturbation theory (TPT1) [M. S. Wertheim, J. Chem. Phys. 87, 7323 (1987)] is extended to model the solid phase of chains whose monomers interact via a Lennard-Jones potential. Such an extension requires the free energy and contact values of the radial distribution function for the Lennard-Jones reference system in the solid phase. Computer simulations have been performed to determine the structural properties of the monomer Lennard-Jones system in the solid phase for a broad range of temperatures and densities. Computer simulations of dimer Lennard-Jones molecules in the solid phase have also been carried out. The theoretical results for the equation of state, the internal energy, and the sublimation curve of the dimer model in the solid phase are in excellent agreement with the simulation data. The extended theory is used to determine the global (solid-liquid-vapor) phase diagram of the LJ dimer model; the theoretical estimate of the triple point temperature for the LJ dimer is T-*=0.653. Similarly, Wertheim's TPT1 is used to determine the global phase diagram of chains formed by up to 8 monomer units. It is found that the calculated triple point temperature is hardly affected by the chain length, and that for large chain lengths the fluid-solid equilibrium coexistence densities are virtually independent of the number of monomers in the chain when the densities are expressed in monomer units. This is in agreement with experimental indications observed in polyethylene, where both the critical and the triple point temperatures tend to finite values for large molecular weights.