Preheat your oven to 425°F for roasting the Brussels sprouts.
Pat the chicken breast dry with a paper towel. Season both sides lightly with salt and pepper.
In a small bowl, mix together balsamic vinegar, olive oil, and minced garlic.
Place the chicken breast in a small baking dish and brush half of the balsamic mixture over it.
In another bowl, toss the halved Brussels sprouts with the remaining balsamic mixture, ensuring they are evenly coated.
Arrange the Brussels sprouts on a baking sheet in a single layer. Roast in the preheated oven for 20-25 minutes, until they are crispy on the edges and tender inside, stirring once halfway through.
While the sprouts are roasting, place the chicken in the oven (or under a broiler for a final glaze if desired) and cook for 18-20 minutes or until the internal temperature reaches 165°F, occasionally basting with any leftover balsamic mixture.
Remove the chicken and Brussels sprouts from the oven. Let the chicken rest for a few minutes before slicing.
Plate the sliced chicken with a generous serving of crispy roasted Brussels sprouts, and enjoy your wholesome, flavorful meal.