cougartxn,
Maybe the first thing to do would be to do some background research on the Chief. If he's the kind who says "no" to everybody andis anti-gun, than you risk placing yourself on his radar in a negative way. You might end up on his "first to question if something weird happens on campus" list. Discreetly ask people who know him, try to find out if there are actually people who have gotten waivers, or get to know him yourself if you cross paths once in a while, asking casual questions that poke around the general gun subject. Find out how he feels about guns to get an idea of how he might respond to your inquiry.
There's plenty of reasons to carry, but the hard part is stating reasons that will work on the Chief.
You can go in, stomp your foot down and demand your 2nd Amendment rights be honored, and very well come across as "one of those militia types." It's my opinion you should leave out the "it's my right" type comments. I would suggest you state, as Tom357 said, that you've passed all the federal, state and local background checks to carry in public.
As a couple others said, don't say anything to suggest that the campus police are unable to do their jobs - you'll just offend him. Get it across that you respect his job and the campus police, but state that the ratio of cops/students means the cops just can't be there for everyone, any maybe you've got really late classes and cross dark lawns and lots.