Preheat the oven to 425°F (220°C).
Toss the Brussels sprouts in half of the olive oil, salt, and pepper, then spread them on a baking sheet.
Peel and chop the sweet potato into 1-inch cubes. Toss with a drizzle of olive oil, salt, and pepper, then spread on a separate baking sheet.
Place the chicken breast on a lightly greased baking tray and season generously with salt and pepper.
Roast the chicken, Brussels sprouts, and sweet potato in the preheated oven. Roast the chicken for about 20-25 minutes until it reaches an internal temperature of 165°F. Roast the Brussels sprouts and sweet potato for about 20-25 minutes until tender and slightly caramelized.
In a small saucepan over medium heat, combine the balsamic vinegar with a splash of water. Bring to a simmer and let reduce for about 3-4 minutes to achieve a lightly thickened glaze.
Once the vegetables and chicken are roasted, drizzle the balsamic glaze over the Brussels sprouts and gently toss to coat.
Slice the chicken breast if desired, then serve with the glazed Brussels sprouts and roasted sweet potatoes on the side.