Authors:Kreidberg et alAbstract:The newly detected Earth-mass planet in the habitable zone of Proxima Centauri could potentially host life - if it has an atmosphere that supports surface liquid water. We show that thermal phase curve observations with the James Webb Space Telescope (JWST) from 5-12 microns can be used to test the existence of such an atmosphere. We predict the thermal variation for a bare rock versus a planet with 35% heat redistribution to the nightside and show that a JWST phase curve measurement can distinguish between these cases at 5σ confidence, assuming photon-limited precision. We also consider the case of an Earth-like atmosphere, and find that the ozone 9.8 micron band could be detected with longer integration times (a few months). We conclude that JWST observations have the potential to put the first constraints on the possibility of life around the nearest star to the Solar System.