Rinse the Chicken pieces under cold running water, then drain and blot dry with paper towels.
Make 1 or 2 deep slashes, to the bone, in each piece, then place in a non- reactive baking dish large enough to hold the pieces in a single layer.
Set aside while you prepare the spice paste.
Combine the garlic, chiles, salt, and pepper in a mortar and pound to a paste with the pestle, then work in the oil; or combine the oil with the other ingredients in a blender and process until smooth.
Using your fingers, stuff half the spice paste into the slashes in each piece of Chicken, then spread the remainder over the skin.
Cover and let marinate, in the refrigerator, for 2 to 12 hours (the longer the better).
Preheat the grill, using the two-tiered method .....Spread one third of the coals in a single layer over one side of the grill, the other tow thirds in a double layer on the other side. Leave a small portion of the grill free of coals. This arrangement gives you a super hot heat source for searing, a moderately hot heat source for cooking, and a warm spot for keeping cooked foods warm. You control the heat by moving the food
When ready to cook the Chicken, oil the grill grate.
Arrange the Chicken pieces, skin side down, on the grate over the hotter section of the grill.
Cook until the skin starts to brown, 3 to 5 minutes.
Move the pieces to the cooler section of the grill and contunue grilling until the skin is more thoroughly browned, 5 to 7 minutes. Move pieces away from flare ups.
Turn the pieces and move them back to the hotter section of the grill. Brown the second side well, 3 to 5 minutes, then move the pieces back to the cooler side to finish cooking. The total cooking time will be 16 to 24 minutes.
When ready, the Chicken will be crisp and golden brown outside and the juices will run clear when the meat is pierced.
Transfer the Chicken to the saucepan with the sauce and bring to a simmer over low heat, spooning the sauce over the Chicken to coat.
Cover and cook until the Chicken is well flavored by the sauce, 4 to 5 minutes.
Transfer the Chicken pieces to serving plates or a platter, spoon the sauce over; and serve.
For a milder marinade and sauce, seed the hot chilies.