Depends on the reason for the chair. You would have to be careful not to compromise skin integrity and restricted access in a stressed situation or in the instance your position is interrupted. I would look into some custom kydex formed to where is easiest accessed with the a for mentioned above considered. Google Wilder tactical holsters he's an sc guy may be able to help out.
You might consider a Sneaky Pete type concealed container. Hide in plain sight and easy to mount. If you need to transfer, merely cover with jacket or shirt as you remove firearm and move from chair or take the Sneaky Pete with you.
Dayman - I've already run into that problem. I usually carry open on my hip right now or with a light jacket concealing the holster. It's definitely not the most advantageous place to carry. I had to remove the side rails from the chair to allow access to my gun. I'll definitely check out Wilson Tactical holsters. Hopefully they'll have something.
Avtomat - Shoulder rigs would work but for two problems. In the summer I'd have to wear a jacket (too hot) and the shoulder rig tends to bind under my arm, scraping my skin. I wouldn't consider an ankle holster. I would need to bend over to get to it and that could easily cause me to topple from my chair. Not a position one wants to be in when the bad guys are around.
Dave - My problem with mounting a holster to the chair is if I'm knocked out of it I lose my gun. Someone could walk up behind me and shove me out of the chair. So there I am on the ground with nothing to defend myself with.
Thanks for the responses, guys. It isn't an easy problem to figure out.