Cover and refrigerate overnight. Remove the pork from the brine, and pat dry.
Heat the smoker to 225 degrees F. Add the wood chunks, and place the pork into the smoker. Cook until the pork reaches an internal temperature of 150 degrees F, 4 to 5 hours.
Once the meat reaches 150 degrees F, heat the oven to 300 degrees F. Wrap the pork in aluminum foil and transfer to a half sheet pan. Place on the center rack and cook until the pork reaches an internal temperature of at least 200 degrees F and is tender and pulling apart easily, 3 to 5 hours. Remove from the oven and rest, covered for 30 minutes before serving.