Remove the neck and giblets from the center of the chicken if it came with them inside.
BRINE: *OPTIONAL Place chicken in a large bowl and cover with water. Add 1/2 cup salt and 1/2 cup sugar to water. Brine from 30 minutes to 4 hours depending on how much time to you have to prepare. Store in refrigerator while brining.
FOR SMOKER: Prepare smoker by piling charcoal on one side of the grill and leaving the other side empty. Soak applewood chips or chunks in water. Remove from water and place in grill. Place a food grate on the grill. Allow to heat to about 250° to 300°. Smoking will take longer than grilling because you'll need to smoke longer at a lower temperature to get the smokey smell in the meat.
FOR GRILL: Prepare the grill by piling charcoal on one side of the grill and leaving the other side empty. For gas grills, turn on half the burners. You'll cook the bird on indirect heat.
FOR THE OVEN: Oven Instructions for Beer Can Chicken: Heat your oven to 350°F. Assemble the bird as directed and place a roasting pan on the lower rack of your oven. Roast at 350°F for about 60 to 90 minutes for a 4 lb chicken.
*Whatever cooking method you use, you have really got to check the internal temperature for doneness. I like this meat thermometer.
PREPARE THE CHICKEN: Remove chicken from brine and rinse. (Discard brine.) Pat chicken dry. Rub butter under the skin and on top of the skin. Sprinkle the salt, pepper, garlic, paprika, and onion under and on top of the chicken.
Place a sturdy pan on the side of the grill or smoker that does not have charcoal on it so that the chicken will get indirect heat. Then, place the chicken upright onto a beer can, fitting the can into the cavity. Pull legs forward to form a tripod, allowing chickens to stand upright.
Smoke covered with the lid, 1 hour and 20 to 40 minutes, depending on the temperature. For Grilling, it should take 60 to 75 minutes, again depends on the temperature. A meat thermometer inserted in the thigh should register 165°F.
Remove from grill and allow chickens to rest for 5 to 10 minutes. Carefully remove beer cans and serve.