Fill your pellet grill or smoker with your choice of fruit wood pellets or chips. Preheat the smoker to 225-250°F (107-121°C).
Pat the chicken dry with paper towels and rub it all over with olive oil.
Apply dry rub generously all over the chicken, inside and out.
Place a drip pan filled with apple juice or chicken broth below the grate to add moisture and catch drippings.
Put the chicken on the smoker, breast side up, and close the lid. Let it smoke for about 3-4 hours, or until the internal temperature reaches 165°F (74°C) in the thickest part of the breast.
Once the chicken is cooked, remove it from the smoker and let it rest until it’s cool enough to handle.
Pull the chicken off the bones and shred it with a fork or with your hands. You can leave the skin on or remove it and chop it up with a knife to add back into the pulled chicken later on.