Pat the chicken fillets dry with kitchen paper and, if you like, brush both sides lightly with olive oil to help the rub stick.
In a small bowl, mix the light brown sugar, smoked paprika, garlic powder, onion powder, sea salt and black pepper until well combined.
Season the chicken fillets on both sides with the rub, pressing it in lightly. For a deeper flavour, chill in the fridge for 30–60 minutes (optional).
Preheat the smoker to 110°C and add apple or cherry wood chips or pellets.
Place the chicken fillets directly on the smoker rack and smoke for 1½–2½ hours, or until an instant-read thermometer inserted into the thickest part reads 74°C.
Remove the chicken from the smoker, loosely tent with tin foil and leave to rest for 5–10 minutes.
Slice or shred the chicken and serve with your favourite sides, or use it in salads and sandwiches.