It has been suggested that the recently discovered exoplanet GJ581d might be able to support liquid water due to its relatively low mass and orbital distance. However, GJ581d receives 35% less stellar energy than Mars and is probably locked in tidal resonance, with extremely low insolation at the poles and possibly a permanent night side. Under such conditions, it is unknown whether any habitable climate on the planet would be able to withstand global glaciation and/or atmospheric collapse. Here we present three-dimensional climate simulations which demonstrate that GJ581d will have a stable atmosphere and surface liquid water for a wide range of plausible cases, making it the first confirmed super-Earth (exoplanet of 2–10 Earth masses) in the habitable zone. We find that atmospheres with over 10 bar CO 2 and varying amounts of background gas (eg, N 2) yield global mean temperatures above 0 C for both land and ocean-covered surfaces. Based on the emitted IR radiation calculated by the model, we propose observational tests that will allow these cases to be distinguished from other possible scenarios in the future.