Preheat an outdoor grill for medium heat. Coat the grill surface lightly with oil. Pour beer into a pan or bowl, and add wood chips. Let soak while the grill heats up.
When the coals are ready, sprinkle the hickory chips over them. Place chicken pieces on the grill, cover, and cook for 15 minutes. Turn over, cover and grill for an additional 15 minutes. Remove the chicken pieces from the grill, and place each leg quarter onto a large square of aluminum foil. Cover with barbeque sauce, and fold the foil into a packet around each piece of chicken.
Return chicken packets to the grill, and cook for an additional 15 minutes per side. Remove packets, and serve with more barbeque sauce.