In shallow glass or plastic dish or in resealable plastic food-storage bag, mix all marinade ingredients. Add chicken; stir to coat with marinade. Cover dish or seal bag; refrigerate at least 30 minutes but no longer than 6 hours to marinate, stirring chicken occasionally.
Heat gas or charcoal grill. Remove chicken from marinade; reserve marinade. On each of 4 (15-inch) metal skewers, thread chicken, bell pepper, zucchini and onion alternately, leaving space between each piece. Brush vegetables with marinade.
Place kabobs on grill over medium heat. Cover grill; cook 10 to 15 minutes, turning and brushing frequently with marinade, until chicken is no longer pink in center. Add asparagus to grill for last 5 minutes of grilling, turning occasionally, until crisp-tender. Discard any remaining marinade.
Sprinkle cheese over kabobs. Serve kabobs with asparagus.