Make the Sweet and Spicy Pickled Vidalia Onions. Place the onion in a bowl and toss with vinegar, salt, cayenne and sugar. Let the mixture stand for at least 30 minutes before serving.
Make the chicken:
In a small bowl, combine the olive oil, mustard, brown sugar, chili powder and garlic.
Season the chicken generously inside and out with salt and pepper. Slather the chicken inside and out with the mustard mixture. Prepare the grill for INDIRECT grilling and preheat to medium-high heat. Pop open the beer can and pour out the top 2 inches of beer. Place the beer can on a solid surface away from the grill. Place the bird cavity over the beer can.
Stand the chicken and beer upright on the grill grate. Close the cover and cook until the juices run clear when the chicken is pierced in the thigh with a fork, about 1 1/4 hours. Remove the chicken from the grill and let stand 10 minutes before carving. Serve with Sweet and Spicy Pickled Vidalia Onions.