In a shallow dish (non-aluminum container) just large enough to hold the chicken breasts, combine the yogurt, olive oil, garlic, lemon zest, mint leaves, cumin, cayenne pepper, and salt; set aside.
Rinse the chicken pieces well and pat dry. Add the chicken to the yogurt marinade, turning to coat both sides; cover with plastic wrap and let marinade in the refrigerator at least 8 hours, preferably 24 hours.
Preheat Barbecue grill. Remove the chicken pieces from the marinade. Place chicken on prepared grill and proceed as follows:
When coals are ready, spread them around the edge of the firebox (24" round) and keep a squirt bottle near the fire to put out flames. Turn the chicken often and do not let them burn. Chicken breasts take about 25 minutes or until a meat thermometer registers an internal temperature of 165 degrees F. (juices will run clear when cut with the tip of a knife). Do not close the lid on the barbecue.
For Gas Barbecue (since you cannot maintain a hot fire without closing lid): Place prepared chicken onto hot grill. Cover barbecue with lid, open any vents, and cook approximately 20 to 25 minutes or until a meat thermometer registers an internal temperature of 165 degrees F. (juices will run clear when cut with the tip of a knife); turning several times during barbecuing.
This is the type of cooking and meat thermometer that I prefer and use in my cooking. I get many readers asking what cooking/meat thermometer that I prefer and use in my cooking and baking. I, personally, use the shown in the photo on the right. To learn more about this excellent thermometer and to also purchase one (if you desire), just click on the underlined: Thermapen Thermometer.
Makes 4 servings.