A completely analytic perturbation theory equation of state for the freely-jointed square-well chain fluid of variable well width (1 less than or equal to h less than or equal to 2) is developed and tested against Monte Carlo simulation data. The equation of state is based on second-order Barker and Henderson perturbation theory to calculate the thermodynamic properties of the reference monomer fluid, and on first-order Wertheim thermodynamic perturbation theory to account for the connectivity of monomers to form chains. By using a recently developed real function expression for the radial distribution function of hard spheres in perturbation theory, we obtain analytic, closed form expressions for the Helmholtz free energy and the radial distribution function of square-well monomers of any well width. This information is used as the reference fluid in the perturbation theory of Wertheim to obtain an analytic equation of state, without adjustable parameters, that leads to good predictions of the compressibility factors and residual internal energies for 4-mer, 8-mer and 16-mer square-well fluids when compared with the simulation results. Further, very good results are obtained when this equation of state with temperature-independent parameters is used to correlate the vapor pressures and critical points of the linear alkanes from methane to n-decane.