Heat oil in a large skillet over medium-high heat. Season chicken with salt and pepper, then cook until golden and cooked through, about 6 minutes per side. Transfer to a plate.
Add balsamic vinegar to the skillet, then add garlic and cook until fragrant, around 1 minute. Add tomatoes, season with salt, and let simmer until soft, about 5 to 7 minutes. Stir in basil.
Return chicken to the skillet, nestle in the tomatoes, and top with mozzarella. Cover with a lid to melt the cheese.
Spoon tomatoes over the chicken and serve hot. Enjoy your flavorful caprese chicken!