Preheat the smoker to 225°F. In a small bowl, mix the brown sugar, paprika, onion powder, thyme, white pepper, mustard powder, coriander, garlic powder, and salt and black pepper to taste.
Pat the chicken breasts dry with a paper towel.
Sprinkle the spices onto the chicken breasts and rub them in.
Place the chicken on a baking sheet and drizzle it with the olive oil. Place it in the smoker for 50 minutes to 1 hour, or until the internal temperature is 165°F.
Cover the tray with aluminum foil and let it rest for 15 minutes. Then remove the foil and serve whole or sliced.