Combine first 7 ingredients in a bowl; stir well. Cover and marinate in refrigerator 1 to 8 hours. Remove chicken from bowl, reserving marinade.
Thread chicken and papaya alternately onto 2 (10-inch) skewers. Prepare grill or broiler. Place kebabs on grill rack or broiler pan coated with cooking spray; cook 7 minutes on each side or until done, basting occasionally with reserved marinade. Serve with black beans and yellow rice.