Isobaric T, x, y data were measured for the quaternary system water + ethanol + ethyl acetate + 1-butyl-3-methylimidazolium acetate at low water mole fractions and at p = 100 kPa. By a procedure presented in this work for systems composed of three volatile components and a nonvolatile ionic liquid (IL), the vapor-phase compositions were obtained by analytical methods and the liquid-phase compositions were calculated with the aid of mass balances. Activity coefficients of the volatile components were obtained without the need of a thermodynamic model of the liquid phase. Enhancement of the relative volatilities by addition of the IL was related with the effect of the IL on the activity coefficients. With the addition of the IL, the activity coefficients of water and ethanol decreased, while the activity coefficient of ethyl acetate increased. The reversed effect of the IL on the activity coefficients resulted in a consistent effect on the relative volatility. At an IL mass fraction of 0.7, the relative volatilities reach appreciable values of 14 for ethyl acetate to ethanol, 84.1 for ethyl acetate to water, and 11.3 for ethanol to water. The VLE data were correlated by the NRTL equation.