1half-full can of locally brewed beer, at room temperature
2Tbspfresh thyme leaves
Prepare your grill for indirect heat. If you are using charcoal, put the coals on one side of the grill. If you are using a gas grill, fire up only half of the burners.
Remove neck and giblets from the cavity of chicken. Rub the chicken all over with olive oil. Mix the salt, pepper, and thyme, then sprinkle it all over the chicken.
If you want, put a sprig of thyme in the beer can. Lower the chicken on to the open 1/2 full can, so that the chicken is sitting upright, with the can in its cavity. Place the chicken on the cool side of the grill, using the legs and beer can to support the chicken on the grill and keep it stable.
Cover the grill. After an hour, check the chicken and refresh the coals if needed. Keep checking the chicken every 15 minutes, until a meat thermometer inserted into the thickest part of the thigh reads 160°F - 165°F. If you don't have a meat thermometer, poke the thigh deeply with a knife, if the juices run clear, not pink, the chicken is done. Cooking times will vary - a 4lb bird will take about 1.5 hours.
Carefully transfer the chicken to a tray or pan. Remember the beer can and the beer inside of it, is hot. Let the chicken rest for 10 minutes. Carefully lift the chicken off of the can. Carve and serve!