If using wood chips, soak them in half the beer mixed with an equal amount of water 1 hour, then drain.
Meanwhile, remove the fat just outside the body cavity of the chicken; discard. Rinse the chicken inside and out, then blot dry with paper towels.
To encourage even browning, rub the chicken all over with vegetable oil, olive oil, or melted butter before applying a BBQ rub.
Sprinkle about 1 tablespoon BBQ Rub inside the body, then rub another tablespoon all over the skin. Cover and refrigerate while you heat the grill to medium (about 350°).
Set up grill for indirect grilling, placing a drip pan below your cooking area. If using a charcoal grill, preheat to medium. If using a gas grill, place all the wood chips in the smoker box and preheat the grill to high; then, when smoke appears, lower heat to medium.
Using a church key-style can opener, make six or seven holes in the top of the beer can. 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 half 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, about 1-1/2 to 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, holding a large metal spatula underneath the beer can for support. (Be careful not to spill hot beer on yourself.) Let stand 5 minutes before carving the meat off the upright carcass.