Gran's Oven-Barbecused Chicken (A Tony Favorite)

1 tablespoon vegetable oil (I use olive oil)
1 medium-size yellow onion, finely chopped
1 cup ketchup
1/4 cup firmly packed light brown sugar
1/4 cup cider vinegar
2 teaspoons Worcestershire sauce
2 teaspoon ground red pepper (optional)
2 teaspoons prepared mustard
2 1/2 to 3 pounds chicken breasts, thighs, and drumsticks (I just use whatever amount of chicken comes in the packet I buy of chicken breasts)

1) Preheat oven to 375. In a small saucepan, heat oil over moderately high heat. Add onion and cook for 5 minutes or until onion is tender. Stir in the ketchup, brown sugar, vinegar, Worcestershire sauce, mustard, and red pepper. Bring to a boil. Lower the heat and simmer, covered, for 10 min.
2) Remove and discard chicken skin. Rinse chicken; drain and pat dry. Arrange chicken in a lightly greased 13x9x2 baking dish. Spoon ketchup mixture over chicken. Bake, covered, for 20 minutes. Uncover and bake 15-20 minutes more or until chicken is cooked through.