Preheat your oven to 350°F. Heat a nonstick skillet with a light coating of oil, then brown the chicken on medium heat. Once browned, move the chicken to a 13x9-inch baking dish that has been coated with cooking spray.
Add more oil to the skillet, then sauté the diced onion until it's tender. Mix in the ketchup, water, vinegar, Worcestershire sauce, brown sugar, mustard, salt, and pepper. Bring this mixture to a boil, then lower the heat and let it simmer, uncovered, for 15 minutes.
Pour the sauce over the chicken in the baking dish. Bake the chicken, uncovered, for 35-45 minutes or until a thermometer shows an internal temperature of 170°F.