Step 1

Brine the chicken: Combine 4 cups water, 2/3 cup salt, and the brown sugar in a medium saucepan. Bring to a boil and whisk until the salt and sugar are completely dissolved. Turn off the heat and transfer to a bowl or pot large enough to submerge the chicken. Stir in 6 cups of ice water and let cool completely. Submerge the chicken in the cooled brine, cover and refrigerate for at least 6 hours or up to overnight.

Step 2

Take the chicken out of the fridge 30 minutes before cooking. Remove from the brine and pat dry completely.

Step 3

Prepare a grill for medium-high indirect heat: For gas grills (with 3 or more burners), turn all the burners to medium-high heat; after about 15 minutes turn off one of the middle burners. For charcoal grills, bank one chimney starter-full of lit and ashed-over charcoal briquettes to one side of the grill. Set up a drip pan on the other side to avoid flare-ups. (Be sure to consult the grill manufacturer's guide for best results.)

Step 4

Whisk together the paprika, onion powder, dried oregano, dried thyme, cayenne, garlic powder, 1/4 teaspoon ground black pepper and the remaining 1/2 teaspoon salt in a small bowl. Brush the chicken all over with the melted butter, and then pat on all of the dry rub mixture.

Step 5

Grill the chicken: Place the chicken breast-side up on the indirect side of the grill, with the legs facing the hotter side of the grill. Cover and cook until an instant-read thermometer reads at least 165 degrees F in the thickest part of the thigh (avoiding the bone), 50 to 60 minutes. The chicken will be quite dark and blackened in spots.

Step 6

Remove from the grill and let rest on a cutting board for at least 20 minutes before carving.