1. Heat oven to 250 degrees F.
2. Cook bacon in large nonstick skillet until crispy, about 4 minutes. Transfer bacon to paper toweling to drain. Drain fat from skillet; wipe skillet clean with paper toweling.
3. Lay chicken breast half on cutting board. With knife blade held parallel to board, slice chicken almost all the way through. Open breast up like a book. Repeat with remaining chicken.
4. Crumble 1 slice bacon on one side of each prepared chicken breast. Top each chicken breast with a quarter of cheese slices, placing slices near fold, leaving 1/2-inch border around edge. Fold chicken breasts over; place on plate. Cover with plastic wrap; freeze 30 minutes.
5. To cook, heat oil and butter in large skillet over medium-high heat. Add onion; cook 2 minutes. Season both sides of chicken with salt and pepper. Push onion to side of skillet; add chicken and cook 5 minutes per side or until lightly browned. Add wine; cover skillet; simmer 15 minutes or until internal temperature of chicken registers 170 degrees F on instant-read thermometer. With tongs, remove chicken to oven-proof plate, leaving onion in skillet; cover chicken with foil; keep warm in 250 degree F oven.
6. Meanwhile, add tomatoes to onion in skillet; cook over medium-high heat 5 minutes or until just softened. Remove chicken from oven; pour any accumulated juices into skillet. Spoon tomato-onion mixture over top of chicken and serve. Makes 4 servings.