Set up a charcoal grill for indirect grilling by piling the hot coals on opposite sides of the grill with a drip pan or large piece of foil in between, or preheat a gas grill to medium.
Put the chicken on a small sheet pan. Combine the remaining ingredients in a small bowl and rub about 3 tablespoons all over the chicken to coat it thoroughly, and put 1 tablespoon into the cavity.
Poke a few holes in the top of an empty 12-ounce beer or beverage can and fill halfway with Prosecco or other sparkling wine, then carefully spoon the remaining rub into the can. (You don't need to use expensive bubbly here, unless of course you happen to be drinking from an open bottle as you start to cook, my personal preference).
Center the cavity end of chicken over the can and slide it in as far as will go before carefully arranging in the middle of the grill rack.
Cover the grill and cook undisturbed for an hour, checking halfway through to be sure your grill temperature remains at a constant temperature between 325 and 350 degrees, adding more coals if needed.
Take the chicken off the grill when the skin is nicely crisp and brown and juices that spew out of the chicken run clear. If you want to be precise, gently insert an instant read thermometer in the thick end of the thigh, without touching bone, to get a reading of 165 to 170 degrees.
Let the chicken rest for at least 10-15 minutes before removing the can, carving and serving.