Combine the vinegar, oil, hot sauce, Worcestershire sauce, salt and garlic powder in a large bowl with 1/2 cup of water. Remove about ¼ cup of the marinade and set aside. Season the chicken with salt and pepper. Add the chicken to the remaining marinade and toss to coat. Refrigerate while you prepare the grill.
Prepare a charcoal fire using about 6 pounds of charcoal and burn until the coals are completely covered with a thin coating of light gray ash, 20–30 minutes. Spread the coals evenly over the grill bottom, position the grill rack above the coals and heat until medium-hot (when you can hold your hand 5 inches above the grill surface for no longer than 3 or 4 seconds). Or, for a gas grill, turn on all burners to high; close the lid and heat until very hot, 10–15 minutes.
Remove the chicken from the refrigerator to take the chill off. Scrape the hot grill rack clean with wire brush. Lightly dip wadded paper towels in the oil; holding the wad with tongs, wipe the grill rack.
Remove the chicken from the marinade; discard marinade. Use the reserved marinade to brush the chicken while cooking. Place the chicken on the grill and cook until seared, about 1–2 minutes per side for legs and thighs, and 3 or so minutes for breasts. Move the chicken to medium-low heat or reduce the heat to medium; continue to grill, turning occasionally and brushing with the reserved marinade, until the juices run clear when pierced, 12–18 minutes.