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He grew the company from one store in 1967 to more than 1,800 locations today and $5 billion in revenue in 2013. The chain surpassed longtime chicken king KFC in U.S. sales in 2012, although KFC is still larger when its foreign stores are factored in.

Cathy slowed down in the past few years. In 2013, his son Dan Cathy assumed the post of chief executive officer and chairman. Truett Cathy became chairman emeritus.

Chick-fil-A caused some controversy in 2012 after Dan Cathy told the Baptist Press that the company backed "the biblical definition of a family," the AP reported. Gay-rights groups held boycotts at Chick-fil-A restaurants.

– The Associated Press contributed to this report.