Thinly slice chicken breasts crosswise and sprinkle with pepper.
In a skillet, heat oil over medium high heat and cook chicken with ginger and garlic for about 5 minutes or until no longer pink inside. Add soy sauce, rice vinegar and hot sauce; remove from heat.
In a large bowl, combine brussel sprouts, onions and carrot. Pour chicken mixture over top and toss well to coat. Stir in chow mein noodles and let stand for 5 minutes to wilt.