Preheat a gas grill, build a charcoal fire, or preheat the oven to 350°F.

Remove the neck and giblets and if desired, rinse the chicken inside and out; pat dry with paper towels. Coat the chicken lightly with the oil and season with salt and pepper.

Open the beer can and drink (or discard) a third of the beer. Place the can on a counter and pick up the chicken with both hands. Slide it over the beer can so that it appears to be “sitting” on the beer can like a throne. If cooking in the oven, place the beer-roosted chicken in a small cake pan, making sure the drumsticks are in front of the can-this will keep chicken stable. If grilling, place the chicken-on-a-can on the cooking grate, away from the heat source, making sure the drumsticks are in front of the chicken-like a tripod.

Cook the chicken, with the lid down, until the juices run clear and an instant-read thermometer inserted in the thickest part of the thigh registers 180°F and 160°F in the breast, about 1¼ hours. If cooking with charcoal, you will need to add more briquettes after 45 to 60 minutes to maintain the heat level. Remove from the oven or grill and let rest for 10 minutes before carving. Leftovers will keep, tightly covered, in the refrigerator for up to 2 days.