In a small bowl stir together 13 c of the mustard 1 Tbsp of the cayenne the vegetable oil and the vinegar
Place the chicken in a large lock-top plastic bag and pour in the mustard mixture
Press out the air and seal the bag tightly
Massage gently to distribute the marinade
Set in a large bowl and refrigerate for at least 2 hours turning and rubbing the bag occasionally
Prepare a fire for indirect-heat cooking in a covered grill
Combine the remaining 13 c mustard with the remaining 1 Tbsp cayenne
Remove the chicken from the marinade allowing as much marinade as possible to cling to the surface Place the chicken skin side down in the center of the grill rack
Grill turning frequently for about 25 minutes do not worry if some of the marinade sticks to the grill
Turn the chicken skin side up and brush it with the mustard-cayenne mixture
Cover the grill open the vents halfway and cook until opaque throughout and the juices run clear about 10 minutes longer
If necessary cut the chicken into smaller portions then transfer to warmed individual plates and serve