1. Combine marinade ingredients in a quart-sized resealable plastic bag, seal tightly, and toss back and forth until well blended. Remove 2 tablespoons mixture, place in a small bowl, and set aside. Add chicken pieces to bag with the remaining marinade, seal tightly, and toss back and forth to coat completely. Refrigerate 1 hour, turning occasionally.
2. Coat grill rack with cooking spray and preheat grill to medium-high heat.
3. Remove chicken from marinade and discard marinade. Thread piece of chicken and each vegetable per skewer in this order: pepper, chicken, tomato, and squash. Repeat with remaining skewers.
4. Place skewers on a grill rack and cook 5 minutes or until chicken is no longer pink in center and juices run clear, turning frequently and being careful not to overcook. Remove from grill, place on a serving platter, and brush reserved 2 tablespoons marinade evenly over all. Serve warm.