High-temperature annealing of gallium arsenide in vacuum causes excess evaporation of arsenic, with accumulation of gallium as liquid droplets on the surface. Using real-time in situ surface electron microscopy, we found that these droplets spontaneously run across the crystal surface. Running droplets have been seen in many systems, but they typically require special surface preparation or gradient forces. In contrast, we show that noncongruent evaporation automatically provides a driving force for running droplets. The motion is predicted and observed to slow and stop near a characteristic temperature, with the speed increasing both below and above this temperature. The same behavior is expected to occur during the evaporation of similar III-V semiconductors such as indium arsenide.