We explore the response of Titan's surface and massive atmosphere to the change in solar spectrum and intensity as the sun evolves into a red giant. Titan's surface temperature is insensitive to insolation increases as the haze-laden atmosphere "puffs up" and blocks more sunlight. However, we find a window of several hundred Myr exists, roughly 6 Gyr from now, when liquid water-ammonia can form oceans on the surface and react with the abundant organic compounds there. The window opens due to a drop in haze production as the ultraviolet flux from the reddening sun plummets. The duration of such a window exceeds the time necessary for life to have begun on Earth. Similar environments, with approximately 200K water-ammonia oceans warmed by methane greenhouses under red stars, are an alternative to the approximately 30OK water-CO2 environments considered the classic "habitable" planet.