van der Waals perturbation theory is used to calculate fluid-solid phase diagrams for a system of perturbed-hard-sphere chains. In both fluid and solid phases, the free energy is the sum of a hard-sphere-chain term as the reference system, and a van der Waals term as the perturbation. The reference system for both phases follows from the Percus-Yevick integral theory coupled with Chiew's results for hard chains. An analytic model for the solid-phase reference term of a hard-chain system agrees well with computer-simulation data for the solid hard-chain compressibility. Simulation data for fluid-solid coexistence curves for hard spheres, and for 4-mer hard chains, are used to fit the reference Helmholtz free energy of the solid phase. The pressure and solid and fluid densities at the hard-chain melting point, predicted by our model, fairly reproduce the available simulation data at different chain lengths. The attractive perturbation term follows from an inverse-power potential with variable exponent n for both fluid and solid phases. The theory here presented reproduces the simulated phase diagrams of chain-like molecules and gives the correct trend for experimental melting points of normal alkanes.