We present the prediction of vapor-liquid-liquid equilibrium (VLLE) from a newly developed PR+COSMOSAC equation of state (EOS). Unlike semiempirical thermodynamic models whose parameters vary with the data used in regression and reparameterization are usually necessary for describing VLLE, this theoretically sound model with its parameters determined from first-principles calculations is not biased against descriptions of either VLE or LLE and can thus be used to predict the occurrence conditions of VLLE. In this model, the molecular interaction and size parameters in the Peng-Robinson EOS are determined directly from a solvation model based on first principle solvation calculations. This new EOS contains neither species dependent parameter nor binary interaction parameters and can be used to predict vapor pressure, liquid density, critical properties of pure substances, and VLE and LLE of mixtures. Without adjustment to the model parameters, this method can predict VLLE with accuracy similar to that of the method modified UNIFAC model. This model is particular useful for the design of new processes involving chemicals whose interaction parameters are not available due to the lack of experimental data.