"Chick-fil-A recently received reports of potential unusual activity involving payment cards used at a few of our restaurants," the company said in a statement Wednesday.
"We are working with leading IT security firms, law enforcement and our payment industry contacts to determine all of the facts."
The company promised that if a security breach was confirmed, it would assume financial responsibility for fraudulent charges to customers' accounts, and arrange for free identity protection services -- including credit monitoring -- for any affected consumer.
US financial institutions have expressed alarm over data breaches affecting a growing number of American retailers.
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"Unfortunately, 2014 has turned out to be the year of the data breach," said Dan Berger, CEO of the National Association of Federal Credit Unions.
Berger cited a massive data breach at Target a year ago, and the similar compromising of consumer information at retailers including Home Depot, Michaels Stores, Neiman Marcus, AOL, eBay and Staples.
"Congress must make passing a national data security standard for retailers a top priority when it returns next week," he said in a statement.