Remove skin, if desired, from chicken quarters. Stir together garlic, marjoram, mustard, salt, and pepper and 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.
Arrange medium-hot coals around a drip pan in a grill with a cover. 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 chicken on a bed of torn mixed greens, if desired. Makes 4 servings.