A person who smokes cigarettes continuously, such that he or she begins a new cigarette as (or almost as) soon as the last one is extinguished. My grandmother died of emphysema after being a chain smoker for most of her adult life.
One who smokes continually by lighting a new cigarette from the one being finished, as in Before they forbade smoking, bridge tournaments often attracted players who are chain smokers . [c. 1930]