In a small bowl, combine olive oil, garlic, Italian seasoning, paprika, salt, and black pepper.
Brush the mixture evenly over both sides of the chicken breasts.
Preheat the grill to medium-high heat and lightly oil the grates.
Place the chicken on the grill and cook for 6 to 7 minutes per side, depending on thickness.
Continue grilling until the internal temperature reaches 165°F (74°C).
Transfer the chicken to a serving platter and allow it to rest for 5 minutes.
Arrange the cherry tomatoes, mozzarella, and fresh basil around and over the grilled chicken.
Drizzle the salad with olive oil and season lightly with salt and pepper if desired.
Finish with a generous drizzle of balsamic glaze over the entire dish.
Serve immediately while the chicken is warm and juicy.