Saturn's giant moon Titan has a thick (1.5 bar) nitrogen atmosphere, which has a temperature structure that is controlled by the absorption of solar and thermal radiation by methane, hydrogen, and organic aerosols into which methane is irreversibly converted by photolysis. Previous studies of Titan's climate evolution have been done with the assumption that the methane abundance was maintained against photolytic depletion throughout Titan's history, either by continuous supply from the interior or by buffering by a surface or near surface reservoir. Radiative-convective and radiative-saturated equilibrium models of Titan's atmosphere show that methane depletion may have allowed Titan's atmosphere to cool so that nitrogen, its main constituent, condenses onto the surface, collapsing Titan into a Triton-like frozen state with a thin atmosphere.