Combine first 4 ingredients in a heavy-duty, zip-top plastic bag; add chicken. Seal bag, and shake until chicken is well coated. Marinate in refrigerator 1 hour, turning bag occasionally. Remove chicken from marinade; discard marinade.
Wash green beans; trim ends, and remove strings. Cut beans diagonally into 1 1/2-inch pieces.
Coat a wok or large nonstick skillet with cooking spray; drizzle 2 teaspoons oil around top of wok, coating sides. Heat at medium-high (375°) until hot. Add green beans, celery, carrot, and onions; stir-fry 5 minutes or until vegetables are crisp-tender. Remove vegetables from wok, and set aside.
Add remaining 1 teaspoon oil to wok. Add chicken; stir-fry 3 to 4 minutes or until chicken is lightly browned.
Combine broth and next 3 ingredients, stirring well. Add broth mixture to wok; stir-fry 1 to 2 minutes or until mixture is thickened and bubbly. Add vegetables and cashews; stir-fry 1 minute or until thoroughly heated. Serve over rice.