Add the balsamic vinegar and brown sugar to a small saucepan. Bring to a gentle simmer over medium heat.
Reduce the heat and simmer, stirring occasionally, until the mixture thickens enough to lightly coat the back of a spoon. Remove from the heat and allow it to cool slightly. It will continue thickening as it cools.
Preheat the grill to medium-high heat.
Season both sides of the chicken breasts evenly with Italian seasoning, garlic powder, onion powder, salt, and black pepper.
Lightly grease the grill grates with a suitable high-heat cooking oil or nonstick grilling spray.
Place the chicken breasts on the hot grill. Cook, turning as needed, until they are nearly cooked through.
Place one slice of mozzarella on top of each chicken breast. Close the grill and continue cooking for a few minutes, until the cheese has melted and the chicken reaches an internal temperature of 165°F (74°C).
Transfer the grilled chicken to serving plates. Top each piece with a fresh tomato slice and sliced basil.
Drizzle the balsamic reduction over the Chicken Caprese Recipe just before serving. Enjoy while the chicken and mozzarella are warm.