I carry out of Houston on Continental all the time. Normally a flawless procedure. One time, however, the counter girl asked to see my CHL. I told her I didn't have one. She looked like she was going to press the hidden bank robber buzzer or something. It was pretty funny. Basically I'm not showing that bimbo my CHL.
I might add that I travel with a Pelican case with some scientific analyzers in it. I have a place cut out in the bottom foam under one of the instruments where the handgun goes. The ammo goes in my main bag. I lock up the pelican case (about the size of a large briefcase) and it sails thru every time.