The Atlanta-based restaurant chain said in a statement Thursday that "unusual activity" involving credit cards was discovered last month.
"We want to assure our customers we are working hard to investigate these events and will share additional facts as we are able to do so," the statement said.
The first report of unusual activity on a customer's card was received Dec. 19, the company said.
The location of the stores in question was not disclosed, but the company said there are a "few." Chick-fil-A operates nearly 1,300 outlets across the U.S.
Attempts to reach the company for additional comment were unsuccessful.