Rinse chicken breasts with cold water, pat dry and place in a large ziplock bag.
In a large nonreactive bowl, mix together all the marinade ingredients and then pour into the bag with the chicken. Squeeze out the excess air and seal. Place in the fridge to marinate for 1 hour.
Place one handful of the wood chips into water to soak for 30 minutes if using a gas grill, otherwise soak all of them to use on a charcoal barbecue.
Prepare the barbeque for indirect cooking. Preheat to high heat on one side.
If using a gas grill, prepare a smoke pouch. Remove the wood chips from the water and squeeze excess water from them. Place them on a large sheet of aluminum foil towards one end, add the remaining dry wood chips and mix together well. Fold the other end over and crimp along all the edges to seal up as a pouch. Poke several holes with a fork in both sides. Place directly over the burner that is on. Close the lid and wait for smoke.
If using a charcoal barbecue, remove the wood chips from the water, squeezing out excess water, and sprinkle them directly onto the hot coals.
Remove the chicken from the marinade and scrape off the excess marinade. Rub the chicken with the 1 tablespoon of olive oil and season with salt and pepper.
When smoke appears, reduce the heat to 220°F Place the chicken on the cool side of the barbecue. Close the lid and smoke for 1 hour. Chicken should have an internal temperature of 170°F; remove and let rest for 5 minutes.