Combine first 8 ingredients in a small bowl; stir well, and set aside.
Coat a wok or large nonstick skillet with cooking spray; drizzle 1/2 teaspoon oil around top of wok. Heat at medium-high (375°) until hot. Add broccoli and carrot; stir-fry 2 minutes. Add zucchini, onion, and green onions; stir-fry 2 minutes. Remove vegetables from wok; set aside.
Add remaining 1 teaspoon oil to wok. Add chicken; stir-fry 3 to 4 minutes or until chicken is lightly browned. Return vegetables to wok. Stir cornstarch mixture; add to wok. Stir-fry 1 minute or until thoroughly heated. Serve over rice.