Remove neck and giblets from chicken and discard. Rinse chicken inside and out, and pat dry with paper towels. Rub chicken inside and out with dry rub. Set aside.
Open beer can and take several gulps (make them big gulps so that the can is half full). Place beer can on top of a small roasting pan (to catch drippings). Grabbing a chicken leg in each hand, plunk the bird cavity over the beer can.
BBQ/GRILL: Cook the chicken over medium-high, indirect heat with the grill cover on, for approximately 1 1/4 hours or until the internal temperature registers 165 degrees in the breast area and 180 degrees in the thigh, or until the thigh juice runs clear when stabbed with a sharp knife. Baste with your favorite barbeque sauce. Remove from grill and let rest for 10 minutes before carving.
OVEN: Preheat oven to 400 degrees. Place the chicken in the oven and roast for 30 minutes. Lower the oven to 325 degrees and roast for 90 minutes basting with the chicken drippings and barbecue sauce until very, very tender. Carefully remove the chicken from the roaster and let rest 10 minutes before carving. Remove beer can from chicken. Serve with more barbecue sauce on the side.