The best source in the world for answers to this question is here:
As to the negative responses here to the idea of OC.... Most of them are completely baseless.
Thugs will steal your gun?
I believe this has been reported all of 2 times in the last 20 years in the US to non-police OC'ers. However, you can't compare those incidents to "normal" OC as I believe in both cases the person had been a prior victim of the thugs that stole their gun. In other words, they were already known to be an easy mark and having a gun didn't change that in the minds of the thugs that already knew them. It would have been entirely different with someone the thugs didn't know.
You will be the first person shot?
The reality is that if thugs see you OC'ing before they actually commit their crime they won't commit the crime at all and so you won't be shot. Both interviews with felons and actual experiences of OC'ers has shown this to be definitively true. Thugs know that if they shoot a police officer they are screwed, and when they see an OC'er they don't know what you are, but assume you may be a police officer, so they don't fark with you.
You can find the rest of the rebuttals on the forums linked above.