I figured it out.. the problem was in the domain set up on the host and domain mapping plugin set up in WP. Here is what I did to get the address bar to display chair.com in the example given.
1. Set up your subsite domains as “parked domains”, not “addon domains” and direct them to your wp installation (in my case, public_html).
2. Create a subdomain for the primary domain you have created in wp (which matches the primary domain on your host) and point that subdomain to the wp installation (public_html in this example).
3. Set up Domain Mapping PlugIn as instructed in the network dashboard.
4. THEN open each subsite dashboard, go to Tools>Domain Mapping and select the url you want as the primary for that subsite. In this example, I had both the subdomain, chair.furniture.com, and the domain, chair.com, to choose from. The subdomain was selected by default. I changed the selection to chair.com and problem solved. Woot!
