Remove and discard the fat just inside the body cavities of the chicken. Remove the package of giblets and set aside for another use. Rinse the chicken inside and out, under cold running water, then drain and blot dry inside and out, with paper towels. Sprinkle 1 tablespoon of the rub inside the body and neck cavities, then rub another 1 tablespoon all over the skin of the bird. If you wish, rub another 1/2 tablespoon of the mixture between the flesh and skin. Cover and refrigerate the chicken while you preheat the grill.
Set up the grill for indirect grilling, placing a drip pan in the center. If using a charcoal grill, preheat it to medium. If using a gas grill, place all the wood chips in the smoker box and preheat to high; then when smoke appears, lower the heat to medium.
Pop the tab on the beer can. Using a 'church key'-style can opener, make 6 or 7 holes in the top of the can. Pour out the top inch of beer, then spoon the remaining dry rub through the holes into the beer. Holding the chicken upright, with the opening of the body cavity down, insert the beer can into the cavity.
When ready to cook, if using charcoal, toss 1/2 the wood chips on the coals. Oil the grill grate. Stand the chicken up in the center of the hot grate, over the drip pan. Spread out the legs to form a sort of tripod, to support the bird.
Cover the grill and cook the chicken until fall-off-the-bone tender, 2 hours. If using charcoal, add 10 to 12 fresh coals per side and the remaining wood chips after 1 hour.
Using tongs, lift the bird to a cutting board or platter, holding a large metal spatula underneath the beer can for support. (Have the board or platter right next to the bird to make the move shorter. Be careful not to spill hot beer on yourself.) Let stand for 5 minutes before carving meat off the upright carcass. (Toss the beer can out along with the carcass.)
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