3 tablespoons olive oil
4 skinless boneless chicken breast halves
1 large red onion, cut into 1/2-inch-thick slices, separated into rings
1 teaspoon chopped fresh oregano or 1/2 teaspoon dried
6 medium-size heads Belgian endive, trimmed, halved lengthwise
1 medium-size head radicchio, cut into 8 wedges
1 tablespoon dark brown sugar
1/2 cup balsamic vinegar
Chopped fresh parsley
Heat 1 tablespoon oil in heavy large skillet over medium-high heat. Season chicken with salt and pepper. Add to skillet; sauté until cooked through, about 6 minutes per side. Transfer chicken to platter (do not clean skillet). Tent chicken with foil.
Heat 2 tablespoons oil in same skillet over medium-high heat. Add onion and oregano; sauté until onion softens, about 10 minutes. Using tongs, transfer onion to plate. Reduce heat to medium. Add endive to skillet and sauté until beginning to brown, turning occasionally, about 5 minutes. Add radicchio. Cover skillet and cook until radicchio begins to brown and endive softens, about 5 minutes. Return onion to skillet. Sprinkle vegetables with sugar. Stir until sugar melts, about 1 minute. Transfer vegetables to plate.
Add vinegar to skillet; boil until slightly thickened, scraping up any browned bits, about 2 minutes. Add chicken to skillet; turn to coat with glaze. Arrange chicken on platter. Arrange vegetables around chicken. Drizzle remaining glaze from skillet over vegetables. Top with parsley.