Place tortillas under the broiler for about 1-2 minutes to toast, turn over and broil 1 more minute to toast other sides. Keep an eye on them so they don’t burn. Remove from oven and set aside.
Place sliced onions on a microwave-safe plate and cook in microwave for 2 minutes, to soften.
Add chicken to a small bowl. Toss with 3 tablespoons barbecue sauce and balsamic vinegar.
To Assemble Pizza: Spread each tortilla with ½ tablespoon barbecue sauce. Use the back of a spoon to spread. Top each with ½ of chicken/barbecue sauce mixture and spread around. Place ½ of the onions all over the top of each pizza. Sprinkle each with ¼ cup tomatoes. Finally, top each with 3 tablespoons of light mozzarella cheese and ½ tablespoon Parmesan cheese.
Place on a baking sheet and broil for about 1-2 minutes until cheese is melted and tortilla is browned. Keep an eye on them so they don’t burn.
Remove from oven. Place each on a dinner plate. Pull apart with your hands into pieces to eat or serve with a fork and sharp knife, if desired.