How do you defumigate an upholstered chair that reeks of cigarette
smoke? I bought a wonderful vintage swivel chair from the 50s or so
(great shape) that is un-sittable -- it smells horrible -- definitely
a smoker's chair.

Some of the advice here might be useful:

http://www.answers.google.com/answers/threadview?id=395856

Something that works wonderfully to remove odors is kitty litter (of
all things!).  I had some potatoes that rotted in my lower cupboards
and could not remove the odor, which was sooooo bad, until I put pans
of kitty litter in several places (at my brilliant son's suggestion).

I'm a firm believer in ozone:

Removing tobacco odor from fine books 
http://answers.google.com/answers/threadview?id=450729

Call large high-end professional rug and upholstery cleaners in your
area and find one that has an in-house ozone chamber. The process may
take up to a week, but I guarantee it will work.

Here's an example of a high-end Upholstery Cleaner in my area that
does this type of work:

D.A. Burns and Sons
http://www.daburns.com/index.html