Brown dwarfs--substellar bodies more massive than planets but not massive enough to initiate the sustained hydrogen fusion that powers self-luminous stars--are born hot and slowly cool as they age. As they cool below about 2,300 kelvin, liquid or crystalline particles composed of calcium aluminates, silicates and iron condense into atmospheric 'dust', which disappears at still cooler temperatures (around 1,300 kelvin). Models to explain this dust dispersal include both an abrupt sinking of the entire cloud deck into the deep, unobservable atmosphere and breakup of the cloud into scattered patches (as seen on Jupiter and Saturn). However, hitherto observations of brown dwarfs have been limited to globally integrated measurements, which can reveal surface inhomogeneities but cannot unambiguously resolve surface features. Here we report a two-dimensional map of a brown dwarf's surface that allows identification of large-scale bright and dark features, indicative of patchy clouds. Monitoring suggests that the characteristic timescale for the evolution of global weather patterns is approximately one day.