Preheat a grill
Brush the radicchio on both sides liberally with the olive oil and sprinkle with salt and pepper to taste. Grill, cut side down first, until just beginning to wilt and brown around the edges, 1 to 2 minutes. Turn to the other side and grill for 1 minute longer. Transfer to a serving platter and serve, drizzled with balsamic vinegar, if desired.