Dissolve salt and sugar with pepper in 1 quart cold water and add with butterflied chicken in a gallon size zipper lock bag and refrigerate for at least 2 hours up to four hours. Remove chicken from bag,rinse thoroughly, pat dry with paper towels.
Pulse olives, olive oil, garlic and capers in food processor until mixture becomes a slightly chunky paste (do not overprocess). Loosen chicken skin and push tapenade under skin of breasts, thighs and legs and season with pepper to taste. At this stage you may also sprinkle with a good BBQ seasoning to taste.
Place chicken bone side down on grill over a medium heat. For a more smoky taste add a few wood chips.
Top chicken at this stage with a flat pan weighted with several bricks and grill until chicken is a deep brown, about 12 minutes.
Remove weighted sheet pan and bricks and flip chicken over with large metal spatula and grill until instant read thermometer reads 160 degrees at the deepest part of the thigh,and juice runs clear, about 12 to 15 minutes longer.
Upon removing chicken to platter, brush both sides with a mixture of honey and fresh lime juice. Cover with foil and let rest for 15 minutes before carving.
NOTE: If you have never butterflied a chicken let your butcher do it for you. Whether a prepackaged whole chicken or one from the butchers case, they will do it for you at no charge. This recipe excels with a butterflied chicken, cut up chicken, well it's just not the same.