In a large saute pan over medium-high heat, warm 1 tablespoon olive oil.
Salt and pepper each chicken breast on both sides and add to pan. Cover and cook for about 15 minutes or so, flipping chicken breasts half way through.
Once chicken breasts has reached 165 degrees F, remove from pan and place on a plate. Cover with foil.
Add 1 tablespoon olive oil to the same pan over medium heat. Add garlic and cook for about 1 minute, scraping the bottom of the pan.
Next add halved tomatoes and saute until the skins soften which should take about 5 minutes or so.
Stir in the chopped basil and add the chicken breasts back to the pan.
Top each chicken breast with 2 slices of the fresh mozzarella. Cover pan with lid and let the mozzarella melt. This should take a few minutes.
Drizzle with a splash of balsamic vinegar and serve!