Vapor-liquid phase diagrams for a bead-spring polymeric model have been calculated for chain lengths of 20, 50, and 100 from Monte Carlo simulations using the recently proposed chain increment method (Kumar et al. Phys. Rev. Lett. 1991, 66, 2935) to determine the chain chemical potentials. Densities of both phases at coexistence and vapor pressures were obtained directly for a range of temperatures from highly subcritical to the vicinity of the critical point, and the critical temperature and density for each chain length were obtained by extrapolation. We also calculated the second virial coefficients for chain-chain interactions of our model and found that the temperature at which the second virial coefficient vanishes for. long chains coincides, within computational uncertainty, with the infinite chain length critical point from our phase equilibrium results. At the critical points of the finite length chains the second virial coefficient assume negative values, indicating attractive interchain interactions. The radius of gyration of chains of varying length was also determined and the theta temperature obtained from the radii of gyration found to coincide, within computational uncertainty, with the critical point for an infinite chain length polymer. The computational methodology we utilize can be extended to the calculation of phase equilibria in multicomponent polymer/solvent systems.