In a bowl, stir together the buttermilk, garlic, rosemary, 2 tablespoons salt, and 2 teaspoons pepper.

Lay the chicken pieces out on two or three baking sheets. Pour half the buttermilk mixture over the chicken; turn the chicken pieces over and pour the remaining buttermilk mixture over them. Refrigerate overnight, turning the chicken pieces now and then.

A half hour before cooking, remove the chicken pieces from the refrigerator. Preheat the grill and coat the grate with olive oil.

Remove the chicken pieces from the baking sheets, patting them dry with paper towels.

Grill the chicken breasts and drumsticks over direct heat for 10 minutes, being sure the skin side faces the heat. Turn and cook over indirect heat, covered, until a thermometer in the thigh reads 165 degrees F., about 15 minutes or so.

Grill the chicken wings over direct heat, turning frequently for about 15 minutes, or until cooked thoroughly.