Light the charcoal briquettes in a chimney starter and let them burn until covered with a light gray ash, about 10-15 minutes.
Meanwhile, assemble the marinade by mixing olive oil, smoked paprika, garlic powder, black pepper, and salt in a bowl.
Rub the marinade all over the chicken pieces, ensuring they are well coated, then set aside briefly to absorb flavors.
Once the charcoal is ready, carefully spread the hot coals evenly on one side of the grill to create a two-zone fire.
Place the chicken on the grill grate, skin side down, over the direct heat zone and sear for 3-4 minutes per side until browned and crispy, listening for the sizzle and watching for grill marks.
Move the chicken to the cooler indirect heat side of the grill, then close the lid. Baste with olive oil occasionally to help develop a crispy exterior while locking in juices.
Position the hot coals so they produce a steady, gentle smoke, adding a handful of soaked wood chips if desired for extra flavor.
Grill the chicken over indirect heat for about 20-25 minutes, flipping occasionally and watching for a dark, crispy, charred exterior.
Check the internal temperature of the chicken; it should reach 165°F (75°C) to be fully cooked and safe, but still juicy.
Remove the chicken from the grill and let it rest for 5 minutes to allow juices to redistribute, resulting in tender, juicy meat with a smoky charred exterior.
Serve hot, sliced or whole, with the crispy, smoky exterior and moist interior ready to enjoy.