Preheat oven to 350°F.
In a large skillet over medium-high heat, heat oil.
Season chicken with salt and pepper on both sides.
Sauté until golden brown, 6 minutes per side. Transfer chicken to a plate.
Add balsamic vinegar to skillet, then add garlic and cook until fragrant, 1 minute.
Add tomatoes and season with salt. Let simmer until soft, 5 to 7 minutes.
Stir in basil.
Return chicken to skillet and nestle in tomatoes.
Top with mozzarella and cover with a lid to melt.
Spoon tomatoes over chicken and serve.