In a bowl, combine the tomatoes, garlic, basil, 1 Tablespoon balsamic, and 1 Tablespoon olive oil. Season to taste with salt and pepper. Leave at room temperature to marinate while you prepare the rest of the ingredients.
Heat 2 Tablespoons olive oil in a large skillet over medium heat. Season the chicken breast with salt and pepper, then add it to the skillet, spreading it out in a single layer. Cook for a few minutes, or until browned on the bottom, then flip and cook an additional few minutes. Remove to a bowl or plate and cover with foil to keep warm.
Meanwhile, preheat the broiler. Brush the cut side of the bread lightly with the final tablespoon of olive oil. Place them oil side up on a baking sheet, then broil on the middle rack for 2-3 minutes, or until just turning brown. As soon as the bread is removed from the oven, rub the toasted side with the halved garlic.
Top with bread with slices of mozzarella cheese and place it back under the broiler for an additional 1-2 minutes or until the cheese is melted and browned in spots.
To serve, top the cheesy bread with the chicken and the bruschetta. Serve with an additional drizzle of balsamic reduction, if desired.