Gibbs ensemble Monte Carlo simulations are reported for the vapor-liquid phase coexistence of argon, krypton, and xenon. The calculations employ accurate two-body potentials in addition to contributions from three-body dispersion interactions resulting from third-order triple-dipole, dipole-dipole-quadrupole, dipole-quadrupole-quadrupole, quadrupole-quadrupole-quadrupole, and fourth-order triple-dipole terms. It is shown that vapor-liquid equilibria are affected substantially by three-body interactions. The addition of three-body interactions results in good overall agreement of theory with experimental data. In particular, the subcritical liquid-phase densities are predicted accurately.