Hi All - thanks for all of your comments. I'm glad my question got people talking.
Unfortunately for me I've had to sit through all the extremely interesting (read boring) termination, discrimination, team building, meetings because I'm in management.
I completely understand that bringing a gun into work would be in violation of the company policy which would make it completely acceptable for them to terminate my employment on the spot.
I suppose I have just two questions:
1) Can an employer search a car that is not on their property? If, as marksman wrote, failure to comply with a search is grounds for termination whether they own the property or not, then it wouldn't matter where the car is parked. In that sense, even if I parked the car in the parking lot next door or 1/2 mile away at Albertson's I could still be terminated if the car contained a firearm. As a sidenote - this is a little scary because an employer technically could terminate an employee for having a gun at home by this logic. In my utterly boring training I learned that companies are terminating employees for failure to stop smoking (even at home) because it costs them money in healthcare premiums. It's true and very scary.
2) However, because the policy clearly states that firearms are prohibited from company property, that I would not be in violation of company policy. I would just be doing something HR didn't like.
While they could still terminate me, they better have a good reason if I'm not in violation of company policy, because thanks to the lovely training they've given me as a manager, I know that unless they can document specific problems with my performance or adherence to policy, that they're putting themselves in a precarious position. While I may nor may not win a trip to court, the lawyer they had teaching our classes stressed that it's important to document everything to avoid the chance that a claim of unlawful termination isn't won (fat, ugly, old, female, pregnant, etc). If they can't prove I violated company policy, well, they must be terminating me for another reason. Perhaps it's discrimination of some sort. I would never do that because I'm not the world's slime, but some people would and that's how our company thinks about terminating employees. The company I work for isn't stupid enough to terminate anyone unless the can document it up the wazoo.
So, is keeping a gun in my car in a parking lot that is not owned by the company (down the street, etc) actually a violation of policy and can they search the car?
Nobody needs to answer - I think I just answered it myself.