Combine sugar and salt in a large bowl and add 3-4 quarts of cold water. Stir to dissolve the sugar and salt in the water. Submerge the chicken in the water and let it soak in the refrigerator for 30-60 minutes.
Combine the zest, oil, 1 tbsp of the rosemary, 1 tbsp of the dijon mustard, 1 tsp of salt and 1 tsp pepper in a small dish. Cover and set aside.
In small saucepan, add the butter, remaining rosemary, mustard, 1 tsp salt and 1 tsp pepper. Cook over low heat until the butter is melted, stirring from time to time to combine. Remove from heat and stir in the lemon juice.
Heat the grill. You can use either an indoor or outdoor grill.
Remove the chicken from the brine and dry with paper towels. Lay the chicken on a large plate or platter and rub it with the lemon zest mixture.
Grill, basting the chicken with the lemon juice and butter mixture as the chicken cooks. Chicken is done when it reaches an internal temperature of 165 degrees, or when there is no pink visible when you cut into a piece.