You see, I had always assumed that was an older store too, but it apparently just dates from the late 1960s. Per my research, until sometime between 1965 and 1970, Safeway was in a former Acme across the street, which is now McDonald's. This is from city directory records, but I'm almost certain I have either an article or an assessor listing that confirms this as well.
http://www.groceteria.com/place/washing ... 1925-1975/
The current Chevy Chase store on Connecticut Avenue dates from the early 1960s. It replaced a store about a block away that is now Magruder's.