Brine the chicken: Rinse the chicken pieces and set aside. In a large bowl or nonreactive pot, dissolve the salt and sugar in 5 cups cold water. Add the spices and zest, if using. Submerge the chicken pieces in the brine, adding more cold water as needed so that the brine covers the chicken. If the chicken tends to bob above the surface, set a plate on top to weight it down. Refrigerate for 2 to 4 hours. Prepare any sauce you like from the recipe links above (or from your own repertoire). Remove the chicken from the brine, discard the brine, quickly rinse the chicken and pat each piece dry with paper towels. If you’re using a rub, put it on the chicken just before you get the fire ready.
Set up your grill: For charcoal, build a medium-hot fire that’s big enough to last for 35 to 40 min. without losing its firepower. This means adding 4 or 5 quarts of charcoal to the starter coals after the fire is started. Once the whole heap is burning nicely and beginning to appear white, arrange the coals so that they only cover about three-quarters of the grill. This way you have a cool spot to move the chicken if it starts to burn or to cook too quickly. If you don’t have a grill rake to even out the coals, you can use a small garden rake or hoe. The fire is ready when you can hold your palm over the main area of the fire for about 3 seconds. For a gas grill, heat all the burners to medium high for 10 to 15 min. before you start grilling.
For a hot fire to last, it needs extra coals. Add 4 to 5 quarts of charcoal so it'll be ready when the first coals die.
A garden rake is handy for arranging coals. cover only three-quarters of the grill with coals; leave a small area "cool."
Cook the chicken: Start the chicken by putting the drumsticks and breasts, skin side up, over the medium-hot part of the fire. Starting skin side up eliminates some risk of initial flare-ups when the fire is at its hottest. (Since thighs and wings take about 5 minutes less to cook, start these later.) Watch the chicken carefully, and if it becomes engulfed in flames from dripping fat, move the pieces to the cooler part of the grill, or turn down the flame on one of the gas grill burners. You want to sear the pieces without charring. When the breasts and drumsticks are beginning to brown, after 5 or 6 minutes, flip them. At this time, put the remaining pieces on the grill, skin side up, and cook them as you did the breasts.
Start the chicken skin side up to avoid early flare-ups. Flip the pieces when they're beginning to brown.
Continue cooking, flipping the pieces every 6 to 8 minutes. If you have an older gas grill that doesn’t exactly crank out the heat and you find that the thicker pieces aren’t cooking through, either close the lid to create more of an ovenlike atmosphere, or plop an old cake pan or disposable aluminum baking pan upside down over the pieces to help retain some of the grill’s heat. Keep in mind, however, that you don’t want to flip or move the chicken pieces too often; this will only slow down the cooking process. The chicken is done when an instant-read thermometer registers 170°F, or when the juices run clear when the chicken is pierced. If you’re not sure, cut into a piece of chicken and take a peek.
Baste, rub, or top grilled chicken with Chipotle-Lime Rub, Maple-Bourbon Glaze, Cucumber-Grape Salsa, or Black Olive & Mint Vinaigrette for extra flavor.