Lightly brush the chicken all over with the oil and season, inside and outside, with the rub.
Prepare the grill for indirect cooking over medium heat (350° to 450°F).
Place a large foil pan on top of the Flavorizer bars, below the cooking grate. Fill it halfway with room temperature water. Prepare the grill for cooking over medium heat (400°F).
Open the beer can and pour off half of the beer. Using a church key–style can opener, make two more holes in the top of the can. Set the can on a flat surface and slide the chicken over the top so the can fits inside the cavity. Transfer the chicken-on-a-can to the grill, keeping the can upright. Carefully balance the chicken on its two legs and the can. Grill over indirect medium heat, with the lid closed, until the juices run clear and the internal temperature reaches 160° to 165°F in the thickest part of the thigh (not touching the bone), 1¼ to 1½ hours.
Open the beer can and pour off half of the beer. Using a church key–style can opener, make two more holes in the top of the can. Set the can on a flat surface and slide the chicken over the top so the can fits inside the cavity. Transfer the chicken-on-a-can to the grill, keeping the can upright. Carefully balance the chicken on its two legs and the can. Grill over indirect medium heat, with the lid closed, until the internal temperature reaches in the thickest part of the breast (not touching the bone), 1¼ to 1½ hours.
Open the beer can and pour off half of the beer. Using a church key–style can opener, make two more holes in the top of the can. Set the can on a flat surface and slide the chicken over the top so the can fits inside the cavity. Transfer the chicken-on-a-can to the grill, keeping the can upright. Carefully balance the chicken on its two legs and the can. Grill above foil pan, over medium heat, with the lid closed, until the internal temperature reaches in the thickest part of the breast (not touching the bone), 1¼ to 1½ hours.
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. Serve warm.
