America’s chickens aren’t multiplying fast enough to keep pace with soaring demand.

Bird breeds used by some of the biggest chicken companies are “producing less eggs,” according to Fabio Sandri, chief executive officer of Pilgrim’s Pride Corp., the No. 2 U.S. poultry producer.

That’s inflaming already rising food inflation, with strong chicken sales at grocery stores and restaurants such as Popeyes Louisiana Kitchen and McDonald’s Corp. embroiled in chicken-sandwich wars. The demand helped Pilgrim’s beat analyst estimates for their second-quarter earnings, released Wednesday.

Chicken breasts at grocery stores have recently been fetching prices around 2015 levels, according to the Bureau of Labor Statistics.

In addition to breeding woes, the American chicken industry that is concentrated largely in the South contended with a severe winter storm in February that killed hundreds of thousands of birds. All told, farmers may struggle to reach the U.S. Department of Agriculture’s forecast for a 1% increase in production for the year.

“Hatchability has been the issue in the industry and that is constraining the industry to exceed the growth that everybody is expecting,” Sandri said Thursday on a call with investors.