In a large pot, combine ingredients for the beer brine, stirring until the sugar dissolves. Place the chicken in the brine and refrigerator overnight (or for at least 8 hours).
When ready to cook, heat grill to high.
In a small bowl, combine salt, brown sugar, paprika, and cayenne pepper to make a dry rub.
Remove the chicken from the brine and pat dry. Apply the dry rub all over the chicken in an even layer. Set aside.
Use a can opener to remove the entire top of the beer can for the chicken. Pour half of the beer into a glass and ENJOY.
Use a can opener to remove the entire top of the beer can. Pour half of the beer into a glass and drink as you prep the chicken.
Place cavity of the chicken onto the open can with the legs pointing down. The open can should support the chicken upright.
Place the can with the chicken on the grill over indirect heat and above the drip pan. Cover the grill and grill chicken for approximately 45 minutes to 1 hour, or until the internal temperature of the thickest part of the thigh registers 165 degrees F. Use the Traeger meat probes to keep track of the temperature!
Let chicken rest 10 minutes before carving.