Preheat the grill.
Cut the radicchio lengthwise into 1/4-inch slices, removing the core. In a small bowl, combine the remaining ingredients to make the marinade. Pour the marinade over the radicchio slices, letting them soak for a few minutes before placing on the grill. Grill for 3 to 4 minutes on each side, continuing to baste with marinade. Remove from the heat and serve.