Where did Ohio Chicken Sandwiches come from? From what I understand, shredded chicken sandwiches are a very regional dish. Some in Ohio have never heard of them, but others eat them at every potluck. They are popular at local diners and restaurants that serve lunch sandwiches. And there are countless ways to make them! The recipe I share below is our favorite, but I’ll share all kinds of variations so you can make these exactly how your family likes.