In large skillet, heat oil over medium-high heat. Add peppers and onions; sauté until softened and lightly browned, about 4-5 minutes. Stir in shredded chicken. Continue cooking until heated through.
Remove chicken and veggies from skillet; wipe out skillet. Keep skillet on medium-high heat. Divide chicken mixture among tortillas. Top with cheese. Fold tortillas in half. Place in skillet, one or two at a time. Cook until golden brown on both sides, about 4-5 minutes.
Cut tortillas into 3 or 4 wedges each. Serve with desired toppings.