For the dry rub: Mix the together the brown sugar, garlic powder, onion powder, smoked paprika, sweet paprika, salt and pepper in a small bowl. Store in a tightly sealed jar.
For the chicken: Preheat your grill to 400 degrees F and set it up for indirect cooking.
Remove the giblet package from the cavity of the chicken and discard. Rinse the chicken and pat dry, inside and out. Rub the chicken, inside and out, with 3 tablespoons of the dry rub.
Open the soda can with a can opener or the tab; make a couple additional holes with a church key opener. Pour out (and drink) half of the soda. Add the garlic cloves and rosemary sprigs to the can. Set the can on a small aluminum tray and place the chicken on top, inserting the can into the empty cavity.
Transfer the chicken, still on the tray, to the grill; close the lid, and cook until the juices run clear, about 1 1/2 hours. Carefully remove the chicken from the grill and allow it to rest for 15 minutes before cutting and serving.
A viewer or guest of the show, who may not be a professional cook, provided this recipe. It has not been tested for home use.