How can I remove cigarette smoke smell from naugahide chair

I would try a leather cleaner, not a protectant. Use a good brand, not armor all. It has been reported before that it is actually hard on things if used a lot. I like the Lexol brand of both vinyl and leather cleaners and conditioners. I was referred to the brand years ago to use on the convertible that I had for the vinyl top and leather seats by someone who reupholstered vinyl and leather in cars, boats, furniture, whatever needed to be done. Use a cleaner, then use a conditioner on it if the smell is gone. If the cushion is zippered, check the cushion to make sure some of the smell isn't coming from there.

First try Murphy's Oil Soap. I know it's primarily for wood, but i will also moisturize the pleather. Otherwise use saddle soap.

In my experience, there is no sure way of removing the smell from leather furniture. Leather is a porous natural material. Unfortunately, it is not only the top outside layer of the leather that has absorbed the smoke.

The smoke chemicals and smell would have also permeated through to the backing, threads, and the inside filling of the chair.

You can try to use cleaners on the outside layer, but eventually the smell going to continue to reak out from the inside.

You might get lucky and tame the smell: http://www.howtocleanstuff.net/how-to-remove-cigarette-smell-from-leather/

I've used repeated applications of Freebreeze on chairs and put in the sun to get rid of the odor. I would give it a good wash with Awesome Orange from the Dollar Tree first and a sponge, and then do your Odor Remover MAX applications also from Dollar Tree

We have a fabric lazyboy recliner that reeked of cigarettes when we bought it second hand. We shampooed it with a steam cleaner and air dryed outside on the deck. If you can air the chair out for awhile after cleaning it might help. We still have the chair after years and it doesn't smell at all anymore. I wonder if patient cleaning and air drying in time the smell will lessen and eventually go away completely.