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 (350° to 450°F). Keep the temperature as close to 400°F 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 put them in the smoker box of a gas grill, following the 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 160° to 165°F, 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.
Carefully remove the chicken-on-a-can from the grill (do not spill the contents of the beer can, as it will be very hot). Let the chicken rest for 10 to 15 minutes (the internal temperature will rise 5 to 10 degrees during this time) before lifting it from the beer can and carving it into serving pieces. Serve warm.