Remove the chicken from the refrigerator. Pat very dry with paper towels. Place on a parchment-lined baking sheet (or similar surface so that you can easily carry it out to the smoker). Brush both sides with the olive oil.
In a small bowl stir together the rub: brown sugar, kosher salt, smoked paprika, garlic powder, onion powder, black pepper, celery salt, and cayenne.
Sprinkle the chicken liberally all over with the dry rub. Let stand at room temperature while you prepare the smoker.
Heat your smoker to 225ºF—if using a charcoal smoker, your fire doesn’t need to be very large. Prior to lighting, add the wood, mixing it with the charcoal. It’s OK if your smoker gets a bit hotter than 225; just note that the chicken will cook more quickly.
Brush the smoker with the canola oil as an insurance policy against sticking. Add the chicken breasts and smoke until they reach 160ºF on an instant read thermometer inserted at the thickest part, 45 minutes to 1 hour depending upon the size of your breasts, your smoker set up, and how much your smoker temperature is fluctuating—check at the 30-minute mark to gauge your progress. Always smoke to temperature, not to time on the clock. The carryover cooking will cause the chicken breast to rise to 165ºF as it rests.
If using butter, melt it in a small bowl. Once the chicken reaches 140 to 150ºF (about 30 or so minutes in), baste the chicken all over the top with the butter to make it extra succulent and delish, then continue smoking until the chicken breast reaches 160ºF, about 15 minutes more.
Remove the chicken from the smoker. Tent with foil and let rest 5 minutes. Slice and enjoy.
Notes
*Feel free to swap the seasoning suggested here with your favorite dry rub.
TO STORE: Store leftovers in an airtight container in the refrigerator for up to 3 days.
TO REHEAT: Loosely cover the chicken breasts with foil and reheat in a 350 degree F oven until warmed through.
TO FREEZE: You can freeze cooked smoked chicken breasts for up to 2 months. Wrap them tightly and place them in an airtight container or freezer bag before freezing. Thaw the smoked chicken breasts overnight in the refrigerator.