Trim any wilted leaves from the radicchio and cut into halves or quarters. Sprinkle the pieces with the oil and vinegar and let marinate about 30 minutes.
Heat the grill or broiler. Lightly sprinkle the radicchio with salt and pepper and grill until slightly browned and cooked through, 4 to 5 minutes each side. Serve with steak, lamb, or chicken, or enjoy it by itself as a warm first course.