Vapor-liquid equilibria (VLE) for solvent-polymer mixtures at modest pressures are obtained from a perturbed hard-sphere-chain equation of state. This equation of state is the sum of a hard-sphere-chain term as the reference system and a van der Waals attractive term as the perturbation. The reference equation follows from the Percus-Yevick integral theory coupled with chain connectivity as described by Chiew. The effect of specific interactions, such as hydrogen bonding, is introduced through the proposal of Veytsman based on the statistical distribution of hydrogen bonds between donor and acceptor sites suggested by molecular structure. Calculated and observed vapor-liquid equilibria are presented for nonpolar, polar, and hydrogen-bonding solvent + homopolymer systems. Pure-component parameters (number of segments per molecule, segment-segment energy, and segment diameter) are obtained from pure-component properties : liquid density and vapor pressure data for normal fluids and pressure-volume-temperature data for polymers. A binary energy interaction parameter must be obtained from limited VLE data for each binary system; this parameter appears to be independent of temperature and composition over a useful range. Theoretical correlations and predictions are in good agreement with experiment.