Preheat the oven to 350 degrees F (175 degrees C).
Place the chicken breasts in a single layer in a 9x13 inch baking dish. In a medium bowl, mix together the brown sugar, paprika, salt, dry mustard, chili powder, vinegar, cayenne pepper, Worcestershire sauce, vegetable juice cocktail, ketchup, water and garlic. Pour the sauce evenly over the chicken breasts.
Bake uncovered, for 35 minutes in the preheated oven. Remove chicken breasts, shred with a fork, and return to the sauce. Bake in the oven for an additional 10 minutes so the chicken can soak up more flavor. Serve on a bed of rice with freshly ground black pepper.