Heat the broth in a large skillet over medium-high heat. Season chicken with salt and pepper, and place in the skillet. Cook 15 minutes, until chicken is almost done.
Place asparagus, red peppers and garlic in skillet. Continue cooking 10 minutes, or until chicken juices run clear and asparagus is tender. Place tomatoes in skillet during last 2 minutes of cook time. Sprinkle with vinegar. Top with mozzarella cheese to serve.