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Prepare your grill for indirect heat: If you are using charcoal, put the coals on one side of the grill, leaving another side free of coals. If you are using a gas grill, fire up only half of the burners.
Season the chicken, rub with oil: Remove neck and giblets from cavity of chicken, if the chicken came with them. Mix the salt, pepper, and thyme in a little bowl, and rub it all over the chicken. Rub the chicken all over with olive oil.
Lower chicken onto half-filled beer can: Make sure the beer can is open, and only half-filled with beer (drink the other half!) If you want, you can put a sprig of thyme (or another herb like rosemary or sage) in the beer can.Lower the chicken on to the open can, so that the chicken is sitting upright, with the can in its cavity.
Grill on indirect heat: Place the chicken on the cool side of the grill, using the legs and beer can as a tripod to support the chicken on the grill and keep it stable.Cover the grill and walk away. Do not even check the chicken for at least an hour. After an hour, check the chicken and refresh the coals if needed (if you are using a charcoal grill).Keep checking the chicken every 15 minutes or so, until a meat thermometer inserted into the thickest part of the thigh reads 160°F - 165°F.The total cooking time will vary depending on the size of your chicken, and the internal temperature of the grill. A 4 lb chicken will usually take around 1 1/2 hours.If you don't have a meat thermometer, a way to tell if the chicken is done is to poke it deeply with a knife (the thigh is a good place to do this), if the juices run clear, not pink, the chicken is done.
Carefully transfer the chicken to a tray or pan: I say "carefully" because the beer can, and the beer inside of it, is quite hot. One way to do this is to slide a metal spatula under the bottom of the beer can. Use tongs to hold the top of the chicken.Lift the chicken, beer can still inside, and move it to a tray. Let the chicken rest for 10 minutes. Carefully lift the chicken off of the can. If it gets stuck, lay the chicken on its side, and pull out the can with tongs.