Cut as much extra fat and loose skin as you can from the chicken. Later when you are grilling it this will help to minimize grease flames burning the chicken.
Split the chicken by cutting down the backbone and opening it to leave the breast attached - flatten out as much as possible while still keeping the chicken in one piece.
Squeeze the juice from the lemon on to the chicken. Mix together the cayenne pepper, black pepper, salt, peeled and crushed garlic, paprika and add to the melted butter; pur and rub this mixture over the chicken.
Refrigerate the chicken (it can be uncovered) for at least an hour or two to let the spices set.
Prepare a gas grill or charcoal grill. For a gas grill heat it to medium temperature. For a charcoal grill, use a modest amount of charcoal to avoid too high of cooking heat. Put the chicken breast side up onto the grill and cover the grill with the lid.
Cook chicken for 30 minutes without turning it. Turn the chicken and cook uncovered for about another 5 to 10 minutes to crisp up the skin.
Remove the chicken from the grill, cut into a thick area (thigh or breast) to make sure it is done, let it cool for 5 minutes and then serve.
Note: if you substitute chicken parts like legs or breasts then the cooking time will be reduced; keep an eye on the chicken and test for doneness before serving.
Get creative: based on the statistics of over 100,000 recipes, here are some other ingredients that are commonly used with the ingredients in this recipe that you might want to experiment by adding one or two of the following (amounts adjusted assuming you making 4 servings):