Combine olive oil, red wine vinegar, cumin, coriander, cinnamon, salt, sugar and cayenne pepper a large glass baking dish. Add all the chicken to the dish, turning to fully coat. Cover tightly and chill for 4 hours.
Bring Wolf grill to medium heat. Grill chicken until just cooked through, brushing periodically with any remaining marinade. Cooking time will be about 10 minutes per side for breasts, and about 12 minutes per side for leg and thigh pieces. Move chicken to platter for serving. Sprinkle with parsley.