The reaction ensemble Monte Carlo (REMC) method [W. R. Smith and B. Triska, J. Chem. Phys. 100, 3019 (1994)] is used to study combined reaction and vapor-liquid equilibrium of the Br-2+Cl-2+BrCl system. The substances are modeled as nonpolar and dipolar two-site Lennard-Jones molecules with Lorentz-Berthelot mixing rules for unlike atoms. No parameters were fitted to any mixture properties in our calculations. The simulated data are compared with experimental results, and with previous simulation data for the mixture obtained by an indirect semigrand ensemble approach. The REMC method efficiently calculates the complete phase compositions, whereas only a limited subset is available experimentally. The agreement of the simulations with experiment is good. In the course of this work, we used the Gibbs ensemble Monte Carlo method (which may be regarded as a special case of the REMC method) to calculate the vapor-liquid equilibrium properties of pure BrCl; since this compound is chemically unstable, such data is experimentally inaccessible.