Yes, but you could get a permit, by law, in California..
Here, in IL, if I were to concealed carry, I'd be commiting a felony and giving up my right to own firearms (and a lot of other things)..
Because I have a Utah permit, and a FFL-03, I follow all rules to the letter.. I can't risk loosing my FFL, as collecting firearms and riding motorcycles are my two pastimes.. (Ok, also shooting competitively, and fishing, and bacon, but you get the point)..
Because I travel for work almost weekly (by plane, mostly) I talk to folks who have been concealed carrying for years. It's very educational, and sometimes a bit scary..