Anywhere from 8 to 48 hours before grilling, remove the giblets from the chicken cavity. Place the chicken, breast side up, on a baking pan that is lined with a baking rack.
In a small bowl, mix together the salt, pepper, brown sugar, smoked paprika, chili powder, dry mustard, and garlic powder.
Sprinkle the rub all over the chicken, including inside the cavity. Use your fingers to press the rub into the skin. Place in the fridge, uncovered, for 8 hours, or even better, 24 to 48 hours.
Remove the chicken from the fridge.
Open the beer and pour out about half of it (feel free to drink it). Carefully place the chicken, upright, onto the can, pushing it all the way down. Pull the legs forward to create a tripod.
Create a 2-zone heat area in your grill (turn one side of your burners on or light your charcoal, and then once they turn ashy, move them over to one side).
Place the beer-can chicken onto the unlit side of the grill. Close the grill and cook until a thermometer inserted into the thickest part of the breast is 165°F, about 1 hour and 45 minutes.
Carefully remove from the grill and place on a baking sheet with a lip (the chicken will release some juices as it rests). Let chicken rest for about 10 minutes.
Transfer the chicken to a cutting board. Use a knife inserted into the top cavity to push the can from the bottom cavity. Carve and serve at once with BBQ sauce.