Whisk together first 5 ingredients and 1/2 cup water in a large shallow dish or zip-top plastic freezer bag; reserve 3/4 cup. Add chicken to dish, turning to coat. Cover or seal, and chill 8 hours, turning occasionally.
Soak wooden skewers in water 30 minutes.
Preheat grill to 350° to 400° (medium-high). Remove chicken from marinade, discarding marinade. Thread chicken, onions, and next 4 ingredients alternately onto wooden skewers, leaving 1/4 inch between pieces.
Grill kabobs, covered with grill lid, over 350° to 400° (medium-high) heat 6 to 8 minutes on each side or until done. Remove from grill, and baste with reserved 3/4 cup marinade.
Spicy Thai Pork Kabobs: Substitute 1 (1.5-lb.) package pork tenderloin, trimmed, for chicken. Proceed with recipe as directed.