Start by patting your chicken breasts dry with paper towels. Season both sides generously with salt and black pepper.
Heat olive oil in your skillet over medium-high heat. Add the chicken breasts and cook undisturbed for about 5-6 minutes per side until golden-brown and nearly cooked through. Remove chicken and set aside.
Lower heat to medium. Add balsamic vinegar and honey to the skillet. Stir and let simmer gently for 3-4 minutes until thickened into a syrupy glaze.
Add halved cherry tomatoes to the skillet, stirring into the glaze to soften slightly. Nestle chicken breasts back in, spoon glaze over top. Cover and cook for 3-4 minutes to meld flavors and finish cooking chicken.
Scatter fresh mozzarella balls over chicken and tomatoes. Cover for about 2 minutes until cheese softens and melts. Remove from heat and sprinkle chopped basil on top.
Serve warm straight from the skillet with extra balsamic glaze and tomatoes. Pairs well with a green salad or crusty bread.