Yes. Response from the NRA (posted by a moderator of the High Road forum): Thank you for your inquiry to the National Firearms Museum. If you are legal in Virginia, you are legal to carry concealed or open carry here in the museum galleries. Please note that we do not permit any photography at this point in time. National Firearms Museum
When I went last week I didn't see any signs prohibiting it. No metal detectors or security screening.
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