Pat chicken breasts dry. Brush with olive oil and season both sides with Italian seasoning, salt, and pepper.
Preheat grill to medium-high heat. Grill chicken for 5 to 7 minutes per side, or until cooked through and grill marks appear.
In the last 2 minutes of grilling, top each chicken breast with a slice of mozzarella and tomato slices. Close the lid to allow the cheese to melt.
Remove chicken from the grill. Sprinkle with fresh basil and drizzle with balsamic glaze.
Serve hot with a fresh salad, pasta, or roasted vegetables.