Sprinkle the salt evenly over the meaty parts of the chicken and inside the cavity (but not on the back). The chicken will be coated with a visible layer of salt. Cover with plastic wrap and refrigerate for 2 hours.
Combine the rub ingredients.
Soak the wood chips in water for at least 30 minutes.
Prepare the grill for indirect cooking over medium heat (180º to 230ºC). Keep the temperature as close to 200ºC as possible throughout the cooking time.
Rinse the chicken with cold water, inside and outside, to remove the salt, and then pat dry with paper towels. Brush the chicken with the oil and season all over, including inside the cavity, with the rub. Fold the wing tips behind the chicken’s back.
Open the can of beer and pour out about two-thirds. Using a church key–style can opener, make two more holes in the top of the can. Place the can on a solid surface and then lower the chicken cavity over the can.
Drain and add two handfuls of wood chips to the charcoal or to the smoker box of a gas grill, following manufacturer’s instructions, and close the lid. When the wood begins to smoke, transfer the chicken-on-a-can to the grill, balancing it on its two legs and the can like a tripod. Cook the chicken over indirect medium heat, 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 70º to 74ºC, 1¼ to 1½ hours. After the first 15 minutes of cooking time, drain and add the remaining wood chips to the charcoal or to the smoker box. If using a charcoal grill, replenish the charcoal as needed to maintain a steady temperature, adding 6 to 10 unlit briquettes after 45 minutes. Leave the lid off the grill for about 5 minutes to help the new briquettes light.
Drain and add two handfuls of wood chips to the charcoal or to the smoker box of a gas grill, following manufacturer’s instructions, and close the lid. When the wood begins to smoke, transfer the chicken-on-a-can to the grill, balancing it on its two legs and the can like a tripod. Cook the chicken over medium heat, 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 70º to 74ºC, 1¼ to 1½ hours. After the first 15 minutes of cooking time, drain and add the remaining wood chips to the charcoal or to the smoker box. If using a charcoal grill, replenish the charcoal as needed to maintain a steady temperature, adding 6 to 10 unlit briquettes after 45 minutes. Leave the lid off the grill for about 5 minutes to help the new briquettes light.
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 a few 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 (the beer will be very hot). Discard the beer. Cut the chicken into serving pieces as desired. Serve warm.
