The generalized Flory dimer (GFD) theory of Hall and co-workers Provides a highly accurate equation of state for hard-chain molecules. It has been extended here to treat chain molecules that interact with a square-well site-site potential by using closed-form expressions for the equations of state for square-well monomer and dimer fluids based on local composition theory and using the analytic solution of the Percus-Yevick theory for monomers and RISM/MSA calculations for dimers. Comparison with Monte Carlo calculations for square-well molecules of lengths 4, 8, and 16 shows that there is very good agreement between this theory and simulation data.