Dear Smriti,
With the chain smokers it's very common & since he is the director he has got the licence to do so.I mean to say he don't have fear from anyone and can do as per his wish.
When you point out the things and you conveyed him then he agreed.Might be he himself don't want to do smoke in office premises but just as you have mentioned he is a chain smoker so he does that, just because of his habit.
Wearing mask and all can be good option but as you are understanding it can hurt his sentiments and can create problem for you.
What I can suggest you is just do meeting with him and try to read his mind and convince him that its neither good for him , his image nor for the company and its employee. If he want to continue his this habit in the same way then you people don't have any option except to tolerate him because he can fire anyone of you and hire the new ones with the condition that no he/she will do the "no smoking campaign".BUT reading your problem I felt that he himself is little bit guilty for that and he understand that you people are not wrong.Even if he want to control that he is not able to do so.
So, what I can suggest you is,make more pamphlets specially for your boss surroundings.Take good printouts from net, show him and ask him frankly that Sir this we have taken out for you , just to remind you "no smoking". So, pls let me know where to pin it.
Also he is director and his time is very valuable so we cannot expect him every time to go out of his office and do smoke.You can decide one or two area where he can smoke - washroom side or in his cabin (decide as per your office layout). This is not to encourage him to do smoking but just to make him to be disciplined and follow rules.
Also I would like to add here that few of your colleagues will be criticizing that in-front of you all but at the same time in front of your director they would be saying that what you people are doing, you are not doing any productive work.So just beware of them.
Just open your eyes and do as you yourself find correct.
Best Wishes
Gunjan