It seems the poultry paucity has arrived, heralded by a series of fast-food executives describing in earnings calls their stores’ struggles to stock enough chicken — nuggets, tenders, wings, patties, all shapes and sizes — to keep pace with legions of peckish Americans. “Demand for the new sandwich has been so strong that, coupled with general tightening in domestic chicken supply, our main challenge has been keeping up with that demand,” said David Gibbs, CEO of Yum Brands, whose KFC restaurants recently rolled out a new fried-chicken sandwich. Charles R. Morrison, chairman and CEO of Wingstop, said this week that “Suppliers are struggling, just as many in our industry are, to hire people to process chicken, thus placing unexpected pressure on the amount of birds that can be processed and negatively affecting supply of all parts of the chicken in the U.S., not just wings.”