Yes, some chicken breeds are in danger of dying out. As we become an increasingly urban society and move away from food production, we’re losing genetic diversity in all of our food crops, plants and animals alike.
The American Livestock Breeds Conservancy (ALBC) focuses on protecting these heritage breeds. A chart listing rare livestock is on their site. If you are a chicken keeper, you can participate in keeping a breed alive by selectively and carefully breeding these rare chickens.
Please note that ordering these breeds from a hatcheries is not the same as actually selectively breeding the birds. ALBC offers guidelines and information for breeding heritage chickens.