I'm not sure if this qualifies as a chain but there are a bunch of them in Florida (or there used to be a few years back).

TooJay's Gourmet Deli. When I was living in South Florida, there were restaurants in Jupiter, Palm Beach Gardens, Palm Beach, Lake Worth, maybe a couple of other cities. I think they've since opened one in Orlando.

I loved almost everything on their menu, especially the pastrami and corned beef sandwiches, "specialized."