Preheat oven to 400 degrees. Pound chicken breasts to even thickness less than 1 inch. Combine chicken and brussels in a bowl, drizzle with oil, and toss to coat.
Arrange chicken and brussels sprouts on sheet pan. Season with Italian seasoning and salt and pepper to taste. Transfer to oven and bake for 10-15 minutes or until chicken is cooked through and brussels sprouts are just barely fork-tender. Meanwhile prepare the glaze.
Add balsamic vinegar to a medium sauce pan. Bring to a boil over medium-high heat and boil for 6-8 minutes until reduced to half the original volume. Remove from heat, stir in honey, garlic powder, and salt. Transfer to a bowl and allow to cool while the chicken finishes cooking.
After chicken and brussels have baked for about 15 minutes, switch to broil for 2-4 minutes (watch carefully so the brussels sprouts don't burn). Remove from oven, drizzle with the balsamic glaze, and garnish with cracked black pepper and fresh thyme if desired and serve.