Preheat your oven to 400°F (200°C). Lightly grease a baking dish with 1 tablespoon of olive oil to prevent sticking. Pat the chicken breasts dry with paper towels and season generously with salt and pepper on both sides.
Place the chicken breasts in the baking dish and drizzle with the remaining tablespoon of olive oil. Scatter the halved cherry tomatoes around the chicken. Roast in the oven for about 20 minutes, or until the chicken is nearly cooked through and the tomatoes start to blister.
Remove the baking dish from the oven. Top each chicken breast with slices of fresh mozzarella and sprinkle the torn basil leaves over the tomatoes and chicken. Return the dish to the oven and bake for another 5-7 minutes, or until the mozzarella has melted beautifully and the chicken reaches an internal temperature of 165°F (75°C).
While the chicken finishes baking, pour the balsamic vinegar into a small saucepan and bring it to a gentle simmer over medium heat. Reduce the heat to low and cook until the vinegar thickens into a syrupy glaze, about 5-7 minutes. Be careful not to burn it.
Drizzle the balsamic reduction over the baked chicken and tomatoes just before serving. Garnish with extra fresh basil if desired. Serve with your favorite sides or alongside pasta dishes for a delightful meal.
