Configurational-bias Monte Carlo simulations in the Gibbs ensemble have been used to perform direct simulations of fluid-phase equilibria in a Langmuir monolayer. The calculations were carried out for a pentadecanoic acid monolayer using the model of Karaborni and Toxvaerd. The results show that the model monolayer exhibits a vapor-liquid coexistence with a critical point at T_c = 104 ± 5 °C and p_c = 1.2 ± 0.2 molecules/nm², but agreement with experimental data is only qualitative. However, the results are of sufficient quality to establish the dimensionality of the model system and to judge between different experimental data sets.