Barbecued Chicken— Spicy Southern Style

5 Tbsp (3 oz) tomato paste
1 tsp ketchup
2 tsp honey
1 tsp molasses
1 tsp Worcestershire sauce
4 tsp white vinegar
3/4 tsp cayenne pepper
1/8 tsp black pepper
1/4 tsp onion powder
2 cloves garlic, minced
1/8 tsp ginger, grated
1 1/2 lb chicken (breasts, drumsticks), skinless