Media report that officers were called to the Bowling Green store early Monday and spokesman Ronnie Ward said they found a man who had been fatally shot outside the restaurant.
Police say the shooting occurred as the result of an attempted armed robbery after the facility closed. There were others inside the building at the time, but no one else was injured. Police weren't sure whether any money was taken.
The identity of the victim wasn't immediately released.
Police are asking anyone with information about the shooting to call Crime Stoppers at 270-781-CLUE.