A lot of the comments here are about the large national chains.
There are many local restaurants that open a second location, then a third, and so on, but are still "local."
One example is In Vinico in the Southwest. A few years ago they had a nice place in Santa Fe, I think it was the only one. A few years later they opened another in Albuquerque. Then over time, one in Denver, Kansas City, etc. now 10, although 4 are in Albuquerque http://ilvicino.com/
Another popular, small, family place is El Parasol around Santa Fe. The family had a more formal place north in Espanola, and a sort of take-out burrito place in Santa Fe. Over time they opened 3 more in the area, sort of fast-food sit downs. But it is still the same family, and still regional.
So, when do you consider a place a "chain"?