Preheat an outdoor grill for medium-high heat, about 375 degrees F (190 degrees C). In a small mixing dish, combine the brown sugar, chili powder, paprika, dry mustard, salt, and ground black pepper. Place the half-full beer can in the center of a dinner plate.
Rinse the chicken under cold running water. Remove the giblets and neck from the chicken; drain and pat dry. Place the entire chicken over the can of beer with its legs on the bottom; keep it upright. 1 teaspoon of the seasoning blend should be sprinkled inside the bird’s cavity. When the seasonings fall into the can, it will begin to foam. The chicken will absorb the flavor of the beer as it cooks.
Place the chicken, standing on the can, on the preheated grill. Grill for 1 hour 15 minutes, or until the juices run clear and the chicken is no longer pink at the bone. Insert an instant-read thermometer into the thickest part of the thigh near the bone and it should read 180 degrees F (82 degrees C).
Remove the chicken from the grill, and carefully remove the can of beer. Discard any liquid still in the can. Serve immediately. Enjoy!