In the suit filed Friday in U.S. District Court in Chicago, Jacksonville, Fla.-based Winn-Dixie Stores and Bi-Lo Holdings allege the companies conspired to fix the price of chickens for nearly a decade, in part by “destroying” their own breeder hens and eggs to hamper production, according to a lawsuit. Since 2008, the coordinated production cuts have resulted in a roughly 50 percent increase in the price of broiler chickens — the most popular kind of chicken meat in the country, according to the lawsuit.