Preheat the oven to 425°F.
Blot the chicken breasts thoroughly with paper towels to remove excess surface moisture.
Set each chicken breast between two pieces of plastic wrap. Using a meat mallet or rolling pin, gently pound the chicken until each piece has a relatively uniform thickness.
Place the prepared chicken breasts in a single layer inside a 9 × 13-inch oven-safe baking dish.
In a small mixing bowl, thoroughly whisk together the balsamic vinegar, honey, olive oil, Dijon mustard, dried basil, salt, black pepper, and finely minced garlic.
Pour the balsamic mixture evenly over the chicken breasts. Turn each piece so that both sides are completely coated with the marinade.
Allow the chicken to marinate for at least 10 minutes before baking.
Cut the cherry or grape tomatoes in half, then distribute them evenly around the marinated chicken breasts in the baking dish.
Transfer the baking dish to the preheated oven and bake for 20–25 minutes, or until the thickest portion of each chicken breast reaches an internal temperature of 165°F.
The tomatoes should become tender and lightly blistered during roasting. Remove the chicken from the oven once it reaches the proper internal temperature to help preserve its moisture.
Remove the baking dish from the oven and allow the chicken to rest for several minutes.
Finish with freshly chopped parsley, then serve the balsamic chicken with the roasted tomatoes and preferred side dishes.