The configuration-bias-vaporization method developed previously for binaries is successfully extended to the simulation of liquid-liquid equilibria of ternary chain molecule systems based on a lattice. The effects of varying the chain lengths and interaction energies on the binodals are examined. Comparisons between simulation results and predictions of the Flory-Huggins theory and the Freed theory are also made. It is shown that the agreement is satisfactory when the compositions are near the corresponding binaries. The discrepancies become larger when the compositions approach the critical consolute point. Generally, the Freed theory gives better agreement than the Flory-Huggins theory. However, improvements are still needed to describe systems near the critical region for both binaries and ternaries.