A little-noticed program that was announced last week by the Global Animal Partnership, a nonprofit that works with farmers and retailers to improve animal welfare, asks chicken farmers to change the breeds of the birds they are raising to a more hardy, slower-growing breed. And it may just have the potential to remake the market for chicken in the United States.

If that sounds like hyperbole, consider this: About a decade ago, the same group persuaded one retailer to buy only cage-free eggs, at a time when keeping laying hens in ranks of small, stacked cages was the only way of doing business. Today, 10 states and 35 major food companies—including McDonald’s, Target, ConAgra and General Mills—have committed to buying only cage-free