Chicken breasts take about 10 minutes to parboil. Legs, thighs and quarters take about five minutes and chicken wings take 15 to 20 minutes. After parboiling, they can be dry-rubbed with seasoning. Heat the grill for 15 minutes and place the chicken on, allowing it to cook for 10 to 15 minutes before turning it over. To cook chicken breast over a grill without parboiling, first place it in a strong zip-lock bag, and then pound it with a rolling pin until it is even in thickness.