Can my Employer ask me to take down my Facebook?

[Sheena]

I have a Facebook, though I do not have it tied to my workplace in any way. It's listed as private through and through, so no part of it is accessible to folks outside my friends list.

I DO NOT have my workplace listed as a company on my facebook, nor do I ever mention or talk about working for said company.

I DO NOT have any coworkers listed as friends, and do not socialize with them outside of the work place. I keep the two very separate.

Recently I received a call from our corporate office, demanding I remove my facebook and delete my account because a picture that I have sets "a bad image for the company" and is"violent and vulgar." It was a picture of my new handgun, which I took training courses for, and is registered and licenced to me.

Since it is my personal media page and is not in any way used to represent my workplace or in any way connected to it, can they legally tell me to remove myself from the social networking site?