This is a great question, Marine, as demonstrated by the logical, intelligent responses.
My automatic response is that gun rights hold sway. On the other hand, do we really want Dwight Schrute walking around the office all day, every day, with a Smith & Wesson.40 strapped to his leg? Even if he's legally obliged to do so? Talk about a hostile work environment.
On the other hand, if some whackjob gets fired and comes back with an "assault" rifle (hat tip to Goshen), wouldn't it be nice if Dwight was also a crack shot and put one in the whackjob's eye before he got started with his massacre?
On the other hand, If I start and run a business, don't I have the right to ask employees to follow my rules? I can order them to please NOT espouse their extremist political views to my customers (true story), but then I'm violating their civil rights, right?
On the other hand, defending my life is a bit more complicated than speaking my mind.
I'll argue either side, but at the end of the day I'm a fan of the second amendment. Too much crazy stuff going on these days, bottom line.
So yes, I'll leave it in the car if they make it a condition of my employment or patronage, because if I agree to their silly no-firearm rule then I'm willfully giving up my right to bear arms.
But no, I'm not going to drive unarmed back and forth to work each day. I drive a chrome Fisker just like Justin Bieber's, and some whackjob high on bath salts is gonna 'jack it and/or eat my face. So no, unless they let me keep it in my car, or they have a weapons cage at the front desk (one that the aforementioned whackjob can't possibly gain access to), then they can kiss my American arse. I'll work/shop/eat/play somewhere else.
I like Jerry's answer best. Don't ask, don't tell.
You won't know I have it until I have to use it, and then you'll be damn glad I had it.