In a small bowl, whisk together butter, lime zest, pepper and salt. Reserve.
Rinse chicken and pat dry. Place chicken in brining bag.
Boil 4 cups of water. Remove from heat. Stir in brining blend, lime wedges, lime zest and juice. Stir in ice cold water. Cool. Pour over chicken. Seal brining bag and refrigerate overnight or 8 hours. Remove chicken from brine and rinse in cold water. Stuff lime pepper butter under skin of chicken breast, legs and wings, being careful not to tear skin. Truss chicken with kitchen twine.
In a small bowl, stir together margarita mix, tequila and Triple sec. Pour mixture into center well of BeeRoaster. Place trussed chicken on BeeRoaster and position in a cast iron skillet. Place skillet on preheated grill.
Close grill and roast for 1 hour or until internal temperature of chicken reaches 165 F. Remove from grill and let rest for 20 minutes. Carve and use on grilled chicken pizza or serve as a main dish.