Build a charcoal fire or preheat a gas grill. In a small bowl, mix the dry ingredients to make the rub. Brush the chicken lightly with olive oil and season with 2 tablespoons rub. Sprinkle the remaining rub inside the cavity of the bird and set aside.
Open the can of beer, pour out about 1/4 cup and punch an extra hole in the top using a bottle opener with a piercing point. Carefully stand the beer can in the center of the grill over indirect medium heat and place the cavity end of the chicken over the beer can.
Close the grill lid and cook the chicken until an instant-read thermometer registers 165 degrees in the breast and 180 degrees in the thigh, 1 to 1 1/2 hours. To remove from the grill, use tongs to hold the chicken steady and slide a large spatula underneath the beer can to keep it stable. Transfer to a work surface and, using the tongs, remove and discard the beer can. Let the chicken rest for 10 minutes before carving.