An Independent Restaurant is one that is not part of a National Chain. They are almost always stand alone properties with the owner working daily IN THE PROPERTY.
Can there be more than one? YES. If the owner and/or founder is involved day to day and the scope is LOCAL in nature. An Independent Restaurant should have a CHEF, but may not if it is something like a burger joint or barbecue shack. All of these places are acceptable.
The Defining Characteristic of an Independent is one that is PART OF A COMMUNITY. Founded here and the money stays here. One that SUPPORTS its community. If the profits are wired hundreds of miles away (or thousands) and no one has ever seen an owner...well...that's a Chain.