Heat barbeque to medium-high heat. Season chicken with salt, pepper and paprika. Lightly-oil grill. Place chicken on bone-side down. Cook 3-4 minutes, and then turn chicken over. Cook a few minutes more, until chicken achieves a nice colour, but is not overly dark.
Move chicken to one side of the barbeque and reduce heat to its lowest setting under it. Reduce heat on the other side to medium. Cover and cook chicken, turning and moving pieces from time to time, for about 30 minutes, or until cooked through. Cut into chicken or check temperature, (which should be 170 degrees F), with an instant read meat thermometer to ensure it is cooked. Baste with barbeque sauce near the ending of cooking.