We predict the existence of a relatively thick (several tens of mbar) N2--CH4 atmosphere on Triton. As on Titan, we find that the organic haze produced by chemical reactions is the most significant factor affecting solar energy deposition. The production of haze material (~10-15 g cm-2 s-10) is obtained by scaling from the Titan value. Collison induced absorption, primarily N2--N2, is the dominant source of thermal infrared opacity. The troposphere is characterized by moist convection and the temperature lapse rate is determined by the saturation vapor relationship of N2 (about 0.25 K km-1). Given Triton's present orbital parameters, one polar cap is receiving sunlight while the other cap is in darkness. Following Trafton (1984) we assume the sublimating pole extends poleward of 35¿ and treat volatile transport as an isobaric process. For nominal values of the surface albedo and emissivity of 0.3 and 0.4, respectively, we find the surface temperature is 59 K (pressure=51 mb). There is a hot stratsophere (T≂130 K) similar to that on Titan due to absorption by the haze. The total opacity of the organic haze (or haze plus N2 cloud) is ≤1. ¿ American Geophysical Union 1989