Place chicken breasts in a large zip lock bag. In a small bowl combine olive oil, balsamic vinegar, lemon juice, salt, pepper, dried basil, and garlic. Pour over chicken and let marinate for at least 1 hour or overnight.
Preheat oven to 400 degrees. Line a baking sheet or large baking dish with parchment paper (or aluminum foil), set aside.
Remove marinated chicken and place on cutting board. Using a small paring knife, make slits horizontally in each chicken, being careful not to go all the way through. You should have 4-5 slits per chicken breast.
Stuff each slit with a peach slice, piece of mozzarella, and a basil leaf. Repeat with remaining slits on each piece of chicken.
Bake for 25-30 minutes or until temperature on thermometer reads 165 degrees F.
Serve warm with balsamic drizzle and extra basil on top.