Type I polar stratospheric clouds (PSCs) are thought to nucleate and grow on stratospheric sulfate aerosols (SSAs). To model this system, thin sulfuric acid films were exposed to water and nitric acid vapors (1 - 3 x 10(-4) Torr H2O and 1 - 2.5 x 10(6) Torr HNO3) and subjected to cooling and heating cycles. FTIR spectroscopy was used to probe the phase of the sulfuric acid and to identify the HNO3/H2O films that condensed. Nitric acid trihydrate (NAT) was observed to grow on crystalline sulfuric acid tetrahydrate (SAT) films. NAT also condensed in/on supercooled H2SO4 films without causing crystallization of the sulfuric acid. This growth is consistent with NAT nucleation from ternary solutions as the first step in PSC formation.