Preheat a grill to medium-low, and brush the grate with oil.
Season both sides of the chicken legs with salt and pepper. Place the chicken on the grill, skin side down, and cook, adjusting the chicken's position and turning the pieces occasionally, until it appears to be about halfway cooked, about 15 minutes. Then use a basting brush to brush the chicken legs with the barbecue sauce, and continue to cook, turning the pieces frequently and reapplying barbecue sauce each time the chicken is turned, until it is cooked through and an instant-read thermometer inserted into the thickest part registers 160 to 165 degrees, 15 to 20 minutes. Serve the chicken hot or warm.
Yield: 6 to 8 servings