Preheat the oven to 375 degrees F. Heat the vegetable oil in a saucepan over medium heat. Add the garlic and cook, stirring constantly, for 1 minute. Add the ketchup, brown sugar, mustard, Worcestershire sauce, vinegar, hot sauce, lemon juice, and cayenne. Bring to a simmer then reduce the heat to low. Cook, stirring frequently, for 15 minutes. Remove the pan from the heat and stir in the liquid smoke. Set the sauce aside. The sauce can be made ahead of time, cooled completely, and stored in the refrigerator in a covered container for up to 3 days. Place the chicken in a single layer in a large roasting pan. Brush the chicken with the olive oil and season with salt and pepper. Cover the pan with foil and place in the oven. Bake at 375 degrees F for 45 minutes. If finishing the chicken on a grill, preheat the grill to medium heat. To finish the chicken in the oven, remove the pan from the oven. Pour off any liquid in the pan. Spread the barbecue sauce over the chicken. Return the pan to the oven and bake at 375 degrees, uncovered, for 15 minutes or until the chicken is done. To finish the chicken on the grill, remove the pan from the oven. Place the chicken on the grill and baste frequently with the barbecue sauce for 15 minutes or until the chicken is cooked through and glazed.