You may need to have it covered professionally but it sounds amazing!
It does sound amazing, it would look great. If you do it, post your project here on Hometalk because I would love to see it!
I agree with Michelle, you may have to get a pro to do it. Unless it is a very basic shape and you can find a slipcover
There are a few faux fur projects here on hometalk, but I suggest looking for a similiar shaped chair on you tube to see how others have recovered chairs https://www.hometalk.com/search/posts?filter=cover%20chair%20faux%20fur
If the cushions are removable, you can make covers much like a pillow cover. If the upholstered parts are attached, you might consider a pro. Sounds cool, I'd do that in a heartbeat!
This post should help. http://thenester.com/2011/03/fur-chair-no-sew-reupholstery.html