In the same pan, add in the Garlic, Chili, and Tomatoes. Add Basil, then mix into the pan. Add in Salt, and Pepper, cover bring to simmer. Reduce heat to medium low. Simmer for 35 minutes, occasionally stirring.
Add Balsamic Vinegar, mix well, then add Chicken back into the pan. Continue to Simmer for 5 minutes, turn Chicken once a minute, stir Sauce.
Place the Cheese over each piece of Chicken. Use enough Cheese to cover each Chicken Breast. Place the lid over the saute pan and continue to cook for about four minutes or until the Mozzarella has melted.
Remove from the heat, remove Chicken. Add Cornstarch to thicken Sauce.