After stripping paint, stain or varnish from a wooden chair, it's nearly always beneficial to sand the chair as well. This process not only removes trace leftovers of whatever you were trying to remove, but it also smooths and evens out any rough spots that may have occurred while you were scraping during the stripping process. This will create a more professional-looking finished product, whether you plan to leave the wood bare or apply new color or varnish.
The more ornate and complex the shape of the furniture, the more likely it is that you'll want to use plain sand paper and sand by hand in order to effectively sand small nooks and crannies in the wood. Though you may be able to use a disc sander on some of the large, flat planes of the furniture, hand sanding will likely give you a more even texture and will be sufficient for the light degree of sanding generally needed on already finished furniture. To expediate the process over semi-flat areas, use a non-electric palm sander.
You may not need to sand if you find that you can remove the varnish, paint or stain thoroughly without sanding, though this will depend on how stubborn these products are. If the chair is delicate or especially thin in certain places, you may not wish to sand it. Also, you may not wish to sand it if the wood is antique and has developed a natural patina (aged color) or other signs of aging that you don't wish to sacrifice through sanding.
You may be able to avoid the need to sand if you can thoroughly remove the stain, paint or varnish without scarring the wood. Apply multiple coats of stripper and scrape with a plastic scraper, if necessary. Alternately scrub with a coarse painting sponge. To counteract some slight roughness to the wood, apply an additional coat or two of varnish to smooth over the coarse spots and seal down areas that might sliver.