1. Adjust oven rack to upper-middle position, about 5 inches from upper heating element; heat oven to 325 degrees. Whisk ketchup, onion, Worcestershire, mustard, molasses, maple syrup, vinegar, chili powder, and cayenne in small bowl; set aside. Season chicken with salt and pepper.
2. Heat oil in heavy-bottomed, nonreactive, 12-inch ovenproof skillet over high heat until beginning to smoke. Brown chicken skinned-side down until very light golden, 1 to 2 minutes; using tongs, turn chicken and brown until very light golden on second side, 1 to 2 minutes longer. Transfer chicken to plate and set aside. Discard fat in skillet; off heat, add sauce mixture and, using a wooden spoon, scrape up browned bits on bottom of skillet. Simmer sauce over medium heat, stirring frequently with heatproof spatula, until sauce is thick and glossy, and spatula leaves clear trail in sauce, about 4 minutes. Off heat, return chicken to skillet, and turn to coat thickly with sauce; set chicken pieces skinned-side up and spoon extra sauce over each piece to create thick coating. Place skillet in oven and cook until thickest parts of chicken breasts register 130 degrees on instant-read thermometer, 10 to 14 minutes. Set oven to broil and continue to cook until thickest parts of chicken breasts register 160 degrees, 5 to 10 minutes longer. Transfer chicken to platter and let rest 5 minutes. Meanwhile, whisk to combine sauce in skillet and transfer to small bowl. Serve chicken, passing extra sauce separately.