mesquite wood chips, soaked in water to cover for at least 30 minutes
Make the rub: in a bowl, combine all the rub ingredients; set aside.
Chickens: remove and discard the neck, giblets, and any excess fat from the chickens.
Rinse the chickens, inside and out, under cold water; pat dry with paper towels.
Remove the backbones and cut each chicken in half.
Coat each chicken half thoroughly with the rub, cover with plastic wrap, and refrigerate for 2-4 hours.
Make the sauce: in a small bowl, whisk the sauce ingredients together along with 1/2 cup water.
Follow your grill’s instructions for using wood chips; grill the chicken halves skin side up, over Indirect Medium heat until the juices run clear and the internal temperature reaches 170° in the breast and 180° in the thickest part of the thigh, about 1 1/4 hours.
Remove from the grill and loosely cover with foil; let rest for about 5 minutes before cutting the halves in two.