Pat chicken breasts dry and rub evenly with olive oil, dried basil, dried oregano, salt, and pepper.
Heat a large skillet over medium heat and sear chicken for 5 to 6 minutes per side until golden and cooked through (165°F internal temperature).
Remove chicken from skillet and set aside.
In the same skillet, sauté diced red onion for 1 to 2 minutes until softened.
Add minced garlic and cook for 30 seconds.
Stir in balsamic vinegar and brown sugar, then simmer for 3 to 4 minutes until thickened and glossy.
Preheat oven to 375°F.
Place cooked chicken on an oven-safe baking sheet or skillet.
Top each breast with sliced tomatoes and mozzarella cheese.
Spoon some balsamic glaze over each piece.
Bake for 5 to 7 minutes until the cheese melts and bubbles slightly.
Sprinkle fresh chiffonade basil over the top and drizzle with remaining balsamic glaze.
Serve hot, ideally with salad, roasted vegetables, or crusty bread.