Did you put the chicken on at the beginning of the smoke? Or did you put it on the last couple of hours?
I ask because most of my smoke wood is spent within the first couple of hours of the burn. I hardly add any smoke wood to the cook, unless i am adding more meat later.
Usually I need to be a bit more careful with chicken as it seems to soak up the smoke flavor faster than most other meats. Then again, I've never tried just doing a chicken breast, it's normally hind quarters, or full chick's for me.