Holding your knife horizontally, insert into the thick end of each chicken breast and cut to make a deep pocket. Be careful not to pierce through the other end.
Stir the cream cheese with the mozzarella cheese, minced sun-dried tomatoes, salt, pepper, and oregano.
Spoon the cheese and sun-dried tomato mixture evenly into the pockets of each chicken breast.
Wrap each stuffed chicken breast with 2 slices of bacon. Place on your smoker rack.
Set the Smoker to 250°F (121°C) using Bradley Flavour Bisquettes of choice (Oak, Maple, or Hickory work great).
Smoke the chicken until they reach an internal temperature of 165°F (74°C).