Combine buttermilk, garlic, herbs, 2 tablespoons salt, and 2 teaspoons pepper.
Divide chicken between 2 baking dishes. Cover with marinade, turning to coat. Refrigerate for at least 4 hours or overnight, turning chicken occasionally. Remove chicken from refrigerator 30 minutes before grilling.
Heat grill to medium with direct and indirect heat zones. Brush grates with oil. Remove chicken from marinade, and pat dry with paper towels. Grill breast halves, thighs, and drumsticks, skin side down, over direct heat for 10 minutes. Flip, move to indirect heat, and grill, covered, until an instant-read thermometer inserted into the thickest part of thighs registers 165 degrees, 10 to 15 minutes. Grill wings over direct heat, flipping often, until cooked through, about 15 minutes.
Serving idea: Grill orange segments and rosemary sprigs over direct heat while the chicken is cooking.