We explore the likelihood of a thick atmosphere around Neptune's satellite Triton. The infrared optical depth in the grey atmosphere approximation is computed for a range of possible surface compositions, albedos, and gravities. If molecular nitrogen and/or hydrogen are present, a self-sustaining optically-thick atmosphere is possible. As such an atmosphere developes, the reradiation of insolation tends toward a uniform global distribution, which provides a strong negative feedback. Bimodal behavior of Triton's atmosphere is therefore possible as seasonal effects and volatile distribution alter the distribution of thermal emission. ¿ American Geophysical Union 1988