Pour half of the beer into a medium bowl. Add the wood chips and stir. Let the wood soak for at least 30 minutes. Use a church key can opener to make two additional holes in the top of the beer can.
In a small bowl mix the rub ingredients.
Prepare the grill for indirect cooking over medium heat (350° to 450°F). If using a charcoal grill, place a large disposable foil pan beside the bed of charcoal and fill three-quarters of the way full with water.
Blot the chicken dry with paper towels. Season the inside of the chicken with 1½ teaspoons of the rub and a pinch inside the neck cavity. Lightly brush the outside of the chicken with oil. Season the outside of the chicken evenly with the remaining rub. Holding the chicken upright, lower it onto the beer can so the can fits inside the cavity, making sure the chicken sits as far down on the can as possible. Tuck the wing tips behind the chicken’s back.
Brush the cooking grates clean. Drain and add the wood chips to the charcoal or to the smoker box of a gas grill, following manufacturer’s instructions. When the wood begins to smoke, transfer the bird-on-a-can to the grill over indirect medium heat (over the drip pan if using a charcoal grill), balancing the bird on its two legs and the can like a tripod. Grill, with the lid closed, until the juices run clear and an instant-read thermometer inserted into the thickest part of the thigh (not touching the bone) registers 160° to 165°F, 1¼ to 1½ hours, rotating once. Using tongs, grasp the bird and slide a sturdy, wide spatula under the beer can. Carefully transfer it in an upright position to a platter and let rest for 5 to 10 minutes (the internal temperature will rise 5 to 10 degrees during this time). Using tongs to hold the chicken and paper towels to hold the can, give the chicken a little twist to loosen the can before trying to remove it. Carefully lift the chicken off the beer can, keeping the can upright to prevent the hot beer from spilling. Cut the chicken into serving pieces as desired. Serve warm.
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