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Combine first 6 ingredients, add chicken. Refrigerate, covered, 4 hours, turning occasionally. Remove chicken from marinade, reserve marinade.
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To Grill: Combine onion and peppers in heavy-duty aluminum foil. Heat marinade to boiling. Grill onion-pepper packet and chicken 5 inches from medium coals for 10 minutes. Turn and baste chicken with reserved marinade until juices run clear (15-17 minutes). Remove chicken, slice diagonally into strips; cover with foil to keep warm. Wrap tortillas in foil, add to grill; continue heating foil packets until vegetables are tender and tortillas are heated through (about 10 minutes).
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To Broil: Broil chicken 4 inches from heat for 4 minutes; turn, broil until juices run clear (4-5 minutes). Slice diagonally into strips; cover with foil to keep warm. In large skillet, heat 3 tablespoons oil; stir-fry onion and peppers until crisp-tender (4-5 minutes). Stir in chicken strips; heat through.
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To Serve: Fill warmed tortillas with chicken strips, onion-pepper mixture and toppings. Roll, serve immediately.