240 W Main St. in McConnelsville, Ohio is an old store in an old building that's a real relic by any measure, but it wasn't always a Kroger and it wasn't even always a supermarket. An article from the Zanesville Times Recorder of 15 Dec. 1967 gives the following information:
3558 Main St. in Weirton, West Virginia is a more likely contender. It opened on 5 June 1956 and is still open in relatively unaltered condition.The newspaper's writers wrote:New Kroger Store
A new Kroger Supermarket will be located and open in February in McConnelsville. The store will be located in the former Bill Janes Chevrolet new car showroom on West Main street, McConnelsville.
Are there any pre-1956 Krogers out there?