Classical theory of binary homogeneous nucleation is extended to the ternary system H2SO4-NH3-H2O. For NH3 mixing ratios exceeding about 1 ppt, the presence of NH3 enhances the binary H2SO4-H2O nucleation rate by several orders of magnitude. The Gibbs free energies of formation of the critical H2SO4-NH3-H2O cluster, as calculated by two independent approaches, are in substantial agreement. The finding that the H2SO4-NH3-H2O ternary nucleation rate is independent of relative humidity over a large range of H2SO4 concentrations has wide atmospheric consequences. The limiting component for ternary H2SO4-NH3-H2O nucleation is, as in the binary H2SO4-H2O case, H2SO4; however, the H2SO4 concentration needed to achieve significant nucleation rates is several orders of magnitude below that required in the binary case. ¿ 1999 American Geophysical Union