To make the balsamic reduction, add balsamic vinegar and brown sugar to a small saucepan over medium heat. Bring to a slight boil and reduce by half, about 6-8 minutes; set aside and let cool.
In a small bowl, combine olive oil, basil and oregano; season with salt and pepper, to taste. Using your fingers or a brush, work the mixture onto both sides of the chicken.
Melt butter in a large oven-proof skillet over medium high heat. Add chicken, skin-side down, and sear both sides until golden brown, about 2-3 minutes per side; drain excess fat.
Place into oven and roast until the chicken is completely cooked through, reaching an internal temperature of 165 degrees F, about 25-30 minutes. Top each chicken with mozzarella cheese. Then broil for 2-3 minutes, or until the cheese has melted completely.
Serve immediately, topped with tomatoes, drizzled with balsamic reduction and garnished with basil, if desired.