In a small saucepan, combine the balsamic vinegar and honey. Bring to a gentle simmer over medium heat, stirring occasionally, until it thickens slightly, about 10-15 minutes. Remove from heat and set aside.
While the balsamic reduction is cooking, season both sides of the chicken breasts with garlic powder, salt, and pepper.
In a large oven-safe skillet, heat olive oil over medium-high heat. Add the chicken breasts and sear for 5-6 minutes on each side, until they are golden brown.
Once the chicken is seared, reduce the heat to low. Add the halved cherry tomatoes and mozzarella balls to the skillet, distributing them around the chicken.
Drizzle half of the balsamic glaze over the chicken, tomatoes, and mozzarella.
Transfer the skillet to the preheated oven and bake for 15-20 minutes, or until the chicken is cooked through and reaches an internal temperature of 165°F (75°C).
Remove the skillet from the oven, drizzle the remaining balsamic glaze over the dish, and garnish with fresh basil leaves before serving.