Cut chicken into 1-inch pieces. Set aside. Remove flowerets from broccoli and cut in half (you should have about 3-1/2 cups). Cut stalks into 1-1/2-inch lengths and then into 1/4-inch strips (you should have about 1-1/2 cups); set aside.
For sauce, in a small bowl combine chicken broth, teriyaki sauce, cornstarch, and sesame oil; set aside.
Add 2 tablespoons cooking oil to a wok or 12-inch skillet. Preheat over medium-high heat (add more oil if necessary during cooking). Stir-fry ginger and garlic in hot oil for 10 seconds. Add broccoli stems; stir-fry for 1 minute. Add broccoli flowerets; stir-fry for 2 to 3 minutes or until crisp-tender. Remove broccoli from wok. Add mushrooms to wok; stir-fry about 1-1/2 minutes or until crisp-tender. Remove from wok. Add bean sprouts and red or green sweet pepper to wok; stir-fry for 1 to 2 minutes or until crisp-tender. Remove from wok. Add chicken to wok. Stir-fry for 4 to 5 minutes or until no longer pink. Push chicken from center of wok.
Stir sauce; add to center of wok. Cook and stir until thickened and bubbly. Return cooked vegetables to wok. Add water chestnuts. Stir to coat. Cook and stir about 2 minutes more or until heated through. Serve immediately over shredded lettuce, if desired. Makes 4 servings.