Cut the chicken into 1-inch cubes and place in a large, shallow, nonmetallic dish. Put all the remaining ingredients, except parsley, in a bowl and whisk together. Pour the marinade over the chicken cubes and toss the meat in the marinade until well coated. Cover and let marinate in the refrigerator for 8 hours or overnight, turning the chicken 2-3 times if possible.
If using wooden skewers, soak the skewers in cold water for about 30 minutes to prevent burning and to keep food from sticking. If using metal skewers, lightly brush with oil. Preheat the broiler or grill pan. Remove the chicken pieces from the marinade, reserving the remaining marinade and thread an equal quantity onto each prepared skewer leaving a little space between each piece.
Brush the broiler rack or grill pan with a little oil. Add the kabobs and cook, turning frequently and brushing with the reserved marinade halfway through cooking, for 15 minutes or until browned on all sides, tender, and cooked through. Serve hot, sprinkled with chopped parsley to garnish.