Combine first 6 ingredients in a large heavy-duty, zip-top plastic bag. Add chicken; seal bag, and shake until chicken is well coated. Marinate chicken in refrigerator 8 hours, turning bag occasionally.
Remove chicken from marinade, reserving marinade. Place marinade in a small saucepan; bring to a boil. Remove from heat, and set aside. Thread chicken evenly onto 4 (12-inch) skewers. Thread zucchini, squash, and sweet red pepper alternately onto 4 additional 12-inch skewers.
Coat grill rack with cooking spray; place on grill over medium-hot coals (350° to 400°). Place vegetable skewers on rack; grill, covered, 5 minutes, turning and basting with reserved marinade. Place chicken skewers on rack; grill chicken and vegetables, covered, 5 additional minutes or until vegetables are tender and chicken is done, turning and basting often with marinade. Remove vegetables and chicken from skewers.
To serve, place 1 cup rice on each plate; top evenly with vegetables and chicken.