In a small bowl combine the dry brine ingredients. Pat the chicken dry with paper towels. Brush the chicken all over with oil and season evenly, inside and outside, with the dry brine. Refrigerate, uncovered, for 24 to 36 hours.
Rinse the chicken briefly under cold running water to remove most of the dry brine. Pat the chicken dry with paper towels and season with the pepper.
Prepare the grill for indirect cooking over medium heat (350° to 450°F).
Truss the chicken: Slide a four-foot length of butcher’s twine under the legs and back. Lift both ends of the twine and cross them between the legs. Then run one end under one drumstick. Run the other end under the other drumstick and pull both ends to draw the drumsticks together. Bring the twine along both sides of the chicken so that it holds the legs and wings against the body. Tie a knot in the ends between the neck and the top of the breast. If necessary, push the breast down a little to expose more of the neck.
Following the grill’s instructions, secure the chicken in the middle of a rotisserie spit, put the spit in place, and turn on the motor. Place a large disposable foil pan underneath the chicken to catch the drippings.
Cook the chicken over indirect medium heat, with the lid closed, until the surface is deep golden brown and the internal temperature reaches 160° to 165°F in the thickest part of the thigh (not toughing the bone), 1¼ to 1½ hours.
When the chicken is fully cooked, turn off the rotisserie motor and remove the spit from the grill. Tilt the chicken upright over the foil pan so that the liquid that has accumulated in the chicken’s cavity pours into the pan. Transfer the chicken to a platter and tent loosely with aluminum foil. Let rest for 5 to 10 minutes (the internal temperature will rise 5 to 10 degrees during this time). Cut into serving pieces. Top with fresh squeezed lime juice and the mint.
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