Pig and cow slaughterhouses are going gangbusters as farmers decide it's too costly to feed their animals with corn that costs nearly $6 a bushel. The resulting glut of protein on the market hog-ties chicken processors' ability to raise prices.

According to an April report from the Department of Agriculture, federal inspectors have seen a 5.9 percent increase in the slaughter of adult female hogs through the first quarter. The amount of pork in cold storage has jumped 25 percent in the last year. Beef slaughter is also at elevated levels.

"Cattle people are losing $100 a head right now," Richard Lobb, a spokesman for the National Chicken Council, said. "They have every incentive in the world to get those animals off of feed and into the market."

Adding to Pilgrim's Pride's woes, the company said it can't find enough containers to carry its chicken legs on cargo ships headed to export markets. Fewer suitable containers are landing on U.S. shores because the weaker dollar is crimping U.S. imports, Bob Wright, the company's chief operating officer, said in a conference call with analysts.

Containers that do arrive here are being diverted to the southern hemisphere to accommodate the suddenly very lucrative trade in rice, wheat, and other grains.

"There is plenty of demand for U.S. chicken in foreign markets," said Rivers. "There simply are not enough containers to move the product in a timely fashion."

Then there's the matter of efficiency, a slaughterhouse version of Moore's Law that could lead to overproduction. Technology that improves the efficiency of inspecting chickens for contamination is helping the industry move toward a standard processing speed of 140 chickens in 60 seconds—birds per minute, in industry parlance—up from the current standard of 71 to 91 b.p.m.

The chicken industry can hope for a reprieve as the weather warms up and the "summer grilling season" begins. Pilgrim's said it expects to see higher prices after Mother's Day, but others aren't sure the industry's woes will end anytime soon.

"We haven't seen the worst of this yet," said the Chicken Council's Lobb. "The chickens are still eating their way through corn that was five bucks or four-fifty."