Brine the chicken breasts (use recipe for Dan Gill's poultry brine) for 30-60 minutes (longer will make the meat mushy). Remove breasts from brine and rinse in cold running water.

Pat dry on paper towels. Marinate breasts in the Italian dressing for 2 hours.

Generously sprinkle on rub on both sides of breasts and under skin if possible.

Smoke chicken breasts 240-250F with strong to medium flavor wood. Mop every 30 minutes on both sides. Remove from smoker when internal temperature in thickest part of breast reaches 155F.