Spray 3- to 4-quart slow cooker with cooking spray. Place chicken in cooker; top with gingerroot, onion and thawed peaches. In small bowl, mix teriyaki sauce and 1/2 cup water; pour over chicken mixture.
Cover; cook on Low heat setting 6 to 7 hours.
Stir thawed broccoli into chicken mixture. In small bowl, mix 1/4 cup water and the cornstarch; stir into chicken mixture. Increase heat setting to High; cover and cook 15 minutes longer or until sauce is slightly thickened.
Meanwhile, in 2-quart saucepan, heat 3 cups water to boiling. Stir in rice. Cover; remove from heat. Let stand 5 minutes. Fluff rice with fork. Serve chicken mixture over rice.