Pound chicken breasts between 2 pieces of plastic wrap to 1/2-inch thickness using flat side of meat mallet or rolling pin
Heat 2 tablespoons oil in ovenproof skillet over medium heat. Add chicken and cook about 3-1/2 minutes per side or until no longer pink in center. Transfer to plate; cover and keep warm
Heat remaining 1 tablespoon oil in same skillet over medium heat. Add onions and garlic; cook and stir 3 minutes. Add tomatoes; bring to a simmer. Return chicken to skillet, spooning onion and tomato mixture over chicken.
Sprinkle cheese over top. Broil 4 to 5 inches from heat until cheese melts.