Heat the oven to 400°F. Starting in a fully preheated oven helps the chicken begin cooking evenly right away.
Rub the chicken all over with olive oil and season it with salt and pepper. The oil helps the skin brown and crisp while the seasoning gives the meat flavor before the sauce goes on.
Arrange the chicken skin side down on a rimmed baking sheet and bake for 25 minutes. This first stretch cooks the chicken without risking burnt sauce and helps render some fat from the skin.
Take the pan out and increase the oven to 425°F, then close the door while the temperature comes back up. Keeping the heat steady makes the next rounds of basting work better and helps the glaze set faster.
Brush barbecue sauce over the exposed side, gently flip each piece with a spatula, sauce the second side, and return the pan to the oven for 7 minutes. The first layer should look shiny rather than thick, and the skin should stay intact as you turn the pieces.
Pull the chicken out again, brush on more sauce over the top, and bake for another 7 minutes. You’ll start to see the glaze darken slightly and turn more glossy as it clings to the chicken.
Brush on the final layer of sauce and bake for 7 more minutes, for 46 minutes total cooking time, then check the internal temperature with a meat thermometer. The chicken should reach at least 165°F in the thickest part, and thighs or drumsticks are especially juicy when they land closer to 180 to 190°F.
Move the rack up and broil for 3 to 5 minutes if you want more color and char. Watch closely here, because the sauce can go from sticky to too dark pretty fast.
Let the chicken rest for about 5 minutes before serving. The juices settle back into the meat, so each bite stays moist instead of running out onto the plate.