The compressibility factors for freely-jointed Lennard-Jones chains are determined in the context of Wertheim's first-order thermodynamic perturbation theory (TPT1). In the TPT1 treatment, nonbonded Lennard-Jones spheres are used as the reference system. The compressibility factors of the chain system, at temperature T*, segment density ρ*, and chain length m, are obtained based on the compressibility factors of the Lennard-Jones spheres, and the density derivative of the radial distribution function, partial derivative ln g(LIS)(σρ*,T*)/partial derivative ρ*, evaluated at the same temperature T* and segment density ρ*. The exact values for these two quantities, obtained from Monte Carlo simulations, are used in our calculations. The TPT1 predictions are found in agreement with Monte Carlo simulation results for the 8-mer, 16-mer, and 32-mer Lennard-Jones chains over a wide range of densities and temperatures. When values of the density derivative of the reference Lennard-Jones sphere system are estimated from the approximate Weeks-Chandler-Andersen perturbation theory, however, the TPT1 predictions do not match the simulation results.