1. Combine marinade ingredients in a bowl. Add chicken and livers and marinate in the refrigerator for 3 hours.
2. Using 12 long (8- to 9- inch) skewers, arrange alternating pieces of chicken, green pepper, mushroom, chicken liver, and the tomatoes.
3. Brush with some of the marinade. Barbecue over charcoal or under broiler in the oven for 15 to 20 minutes, brushing with marinade and turning frequently.