To make oven-roasted barbecue chicken, mix together 1/2 cup ketchup, 1/2 cup honey, 1/4 cup red wine vinegar and 4 minced cloves of garlic. Cover the sauce, and refrigerate it for one hour. Heat 4 tablespoons of olive oil in a skillet, and use this to cook 6 chicken pieces for two to three minutes per side. Transfer the chicken to a baking dish, cover it with the sauce, and bake at 350 degrees F for 35 to 45 minutes.
Alternatively, you can make barbecue chicken drumsticks with a homemade sauce that's flavored with chili powder and dry mustard. Begin by combining 1/2 cup water, 1/3 cup ketchup, 1/3 cup white vinegar, 1/4 cup brown sugar, 4 teaspoons butter, 2 teaspoons salt, 2 teaspoons Worcestershire sauce, 2 teaspoons dry mustard and 2 teaspoons chili powder in a mixing bowl. You can add more or less chili powder and Worcestershire sauce according to taste. Stir well.
Place 6 chicken drumsticks in a baking dish. Pour the sauce over the drumsticks, and cover the pan with foil. Place the chicken in an oven that has been preheated to 400 degrees F, and bake for approximately one hour, turning the chicken over halfway though cooking. Make sure a meat thermometer reads 165 degrees F when inserted near the bone.