Hundreds of circumstellar disks in the Orion nebula are being rapidly destroyed by the intense ultraviolet radiation produced by nearby bright stars. These young, million-year-old disks may not survive long enough to form planetary systems. Nevertheless, the first stage of planet formation-the growth of dust grains into larger particles-may have begun in these systems. Observational evidence for these large particles in Orion's disks is presented. A model of grain evolution in externally irradiated protoplanetary disks is developed and predicts rapid particle size evolution and sharp outer disk boundaries. We discuss implications for the formation rates of planetary systems.