Heat oil or butter in heavy skillet over medium high heat. Sauté chicken until just done and set aside.
Add oil or butter to skillet and sauté onions, celery. After onions are softening slightly, add peppers, mushrooms, bamboo and chestnuts. Sauté until tender crisp. Add broth and soy sauce and simmer on low for 5 minutes. Stir in cashews. Add salt and pepper to taste.
In separate bowl, combine cornstarch and water and blend slowly into simmering mixture and heat through until thick.
Serve over rice or noodles if desired.