Preheat oven to 350 degrees F.
Season chicken on both sides with 1 Tbsp. oil, basil, oregano, salt and pepper.
Heat a large oven-proof skillet over medium-high heat. Once hot, add remaining oil, then chicken, and sear chicken quickly, flipping once, just until golden on both sides. Remove to plate.
Mix together the diced red onion, garlic, balsamic vinegar and brown sugar. Pour the mixture into the skillet and simmer, stirring, for 3 minutes.
Return chicken to pan and spoon sauce over it. Place pan in oven and roast until the chicken is cooked through (165 degrees), about 10-20 minutes depending on how thick the breasts are. Remove from oven.
Turn oven to broil.
Top each chicken with a slice of fresh mozzarella cheese. Broil just until the cheese has melted.
Serve immediately, topped with fresh sliced tomatoes and fresh-cut basil and spoon the pan sauce over the top.
Make it a meal and serve chicken caprese with a green salad and fresh artisan bread.
