Remove skin from chicken, if desired. Pat chicken dry with paper towels. Stir together garlic, marjoram, mustard, salt, and pepper; rub mixture into chicken pieces. Combine honey and vinegar; lightly brush over entire surface of chicken pieces. Cover chicken and refrigerate for at least 2 hours.
In a grill with a cover, arrange medium-hot coals around a drip pan. Test for medium heat above the pan. Place chicken pieces, bone side down, on the grill rack over the drip pan. Cover and grill for 50 to 60 minutes or until chicken is tender and juices run clear, adding more coals as necessary to maintain heat. Serve grilled chicken pieces on a bed of torn mixed greens, if desired. Makes 4 servings.