Preheat oven to 350F.
In a 9×13 glass baking dish, whisk together the balsamic vinegar, honey, soy sauce, and minced garlic. Place the chicken breasts on top of the mixture and turn to coat.
Bake, uncovered, for 30-40 minutes, depending on the size of the chicken breasts, until cooked through. Baste the chicken with the sauce half way through cooking.
Note: Can be marinated up to 8 hours ahead of time.