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The night before or 8 or more hours ahead of time, rub chicken all over with sea salt. Cover loosely and set in fridge.
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One hour before cooking, combine all dry rub ingredients. Set halved chicken skin side up on a tray and rub prepared dry rub into chicken skin (use just about all of the rub – you may have a few tablespoons leftover). Cover and set in fridge.
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In a standard kettle charcoal grill, prepare hot coals in a charcoal chimney (or using your preferred method). While coals are heating, soak 2 handfuls of hickory chips in a bowl of water. Once coals are all gray and very hot, bank them to one side (this creates a zone of indirect heat). Set a small aluminum pan filled with water on the other side. Sprinkle soaked hickory chips on coals and set grill grate in place. Place chicken halves skin side-up on grill grate as far from coals as possible. Cover grill with lid vent half open. When smoke dies down, add a handful of dry hickory chips (likely 1 - 2 more times during cook time). Cook chicken 1 1/2 - 2 hours, checking temperature after 1 hour. To check temperature, insert thermometer into the space where the thigh meets the breast and pull when temp reaches 170 degrees F. Rest chicken a few minutes until it’s cool enough to carve without burning yourself.
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To serve, slice the thigh and leg away from the breast. Then slice the drumstick from the thigh at the joint. Cut wing from the breast, chop off wingtip, and discard. If you prefer, cut breasts in half to make each into two small pieces, though you can also leave breasts whole. Serve immediately.