Pound the chicken breasts slightly, so that they are of even thickness (do not pound them completely flat like for chicken cutlets). To do that place a piece of baking paper or thick plastic foil over the meat and pound them lightly with a meat mallet or a rolling pin.
Season the chicken with salt, pepper, Italian seasoning, and garlic powder on both sides.
Heat the oil on a frying pan over high heat. Place the chicken in the pan. Cook until golden browned on one side then flip over and place mozzarella slices on top. Cover the pan with a lid and cook over medium-low heat until the cheese is lightly melted and the chicken is cooked through.
Take the chicken off the pan, place tomato slices on top and let stand for 5 minutes.
Make the balsamic sauce (balsamic reduction): To make the balsamic reduction you need to cook the balsamic vinegar until it reduces its volume and it's thick and syrupy. Whisk it constantly making sure it doesn't stick to the bottom of the pan. You can do that in a small saucepan or just directly in the pan where you were cooking your chicken. This way the sauce will be more flavorfull (juices from the chicken + brown bits from the bottom of the pan) but the sauce needs to be strained through a sieve.
Cut the basil leaves into slices and sprinkle them over the tomatoes.
Drizzle the chicken breast with balsamic reduction.