Prepare the rub. Mix all of the rub ingredients together. Break up the clumps. Taste the rub to make sure you like the taste, adjust accordingly.
Unwrap the pork roast and place it on butcher paper or in a pan that can catch the rub. With clean hands work the rub mixture into and all over the pork shoulder. Be generous with the amount of rub to maximize the flavor of the pork. Wrap it in plastic or butcher paper, place it in a pan and refrigerate overnight.
Place the wood chips into a bowl and cover them with water to soak overnight.
Take pork out of refrigerator and let sit for 1 to 2 hours to bring it to room temperature.
Next, prepare your grill to smoke the pork. Remove one of the grill grates on one side of the grill--this is where the wood chips will go. The pork shoulder will sit on the other half of the grill to cook by indirect heat.
Place an aluminum tray of water on the grill to help moderate the heat and prevent drying of the pork. The best place for it is on the upper rack if you have one.
Next create a double layered aluminum foil boat with a handful of wood chips in it. Place it directly on the burner on the side of the grill without a grate.
Turn the grill on to medium flame, cover the grill and let it heat up until the wood chips start to smoke.
Once the grill is smoking, place the pork on the grill grates away from the direct heat. If the roast has a fatty side, place it facing up. Then cover the grill, lower the flame, and let the cooking begin. The temperature you want to maintain is around 225F.
To maintain the smoke for around 4 hours you will need to check the grill. The temp should stay between 210F-240F. Check to make sure the wood chips are smoking every half hour. Once an hour you will likely need to add more wood chips to the pile. Cooking time for your roast should be 90 minutes per pound. Regular sized 4 pound roast should take at least 6 hours.
After about 2 hours of cooking, reposition the roast so the side facing the heat is positioned away from it.
After 5 hours, check the internal temperature. You can safely eat it at any internal temp above 145°F, but for a great pulled pork it needs to be around 195°F.
When the meat reaches 195°F, remove it from the heat, tent it loosely with foil over a cutting board (to catch the juices) and let it rest for at least 30 minutes. If after 6 hours of cooking the meat hasn't reached 195°F internal temp, try finishing in the oven.
To finish in the oven, wrap the roast in aluminum foil to help prevent it from drying out and place it in a roasting pan set it in the oven at 300°F. Cook until the internal temperature of the roast reaches 195°F. When it reaches temperature, remove the roast from the oven and let rest for at least 30 minutes.
Pull the pork apart with 2 forks. Only now do you add any barbecue sauce (and any accumulated juices) to the meat. Taste it first: It might not need sauce at all, and if it does, add only a little at a time.