The development of a Turing instability to a spatially modulated state in a photoexcited electron-hole system is proposed as a novel signature of exciton Bose statistics. Recent work shows that such an instability, driven by kinetics of exciton formation, can result from stimulated processes that build up near quantum degeneracy. The stability of an electron-hole interface which describes recently observed exciton rings is analyzed. Interface instability occurs below a critical temperature, with a periodic 1D pattern developing via a continuous (type II) transition, in a qualitative agreement with observations.