Hi there,
Although an intermittent problem with your ignition switch, or safety switch, or battery is not out of the question, I think your car is having the same attitude problem as many (many, many) other cars equiped with PASSLOCK (theft deterrent system).
Is your security light on when that happen? (blinking maybe?)
In a lot of cases, when your car doesn't start, you can usually wait 10 minutes, and it will start right up.
You can find a lot of posts about this issue online. I suggest you do some research about this before you go to a chevy dealer. A dealer would likely diagnose a bad BCM, or bad ignition switch, bad passlock sensor, or bad starter, etc, etc, and leave you with a much lighter wallet if you know what I mean.
They are ways to actually trick the passlock system without changing all kind of parts and spending mucho dinero…
Basically, when you put your key in the ignition and turn it, it sends a low voltage signal to your BCM (body control module) that ‘analyses’ it. If this low voltage signal is within specification, the BCM allows your car to start. Well, sometime this signal gets lost somehow or is not within specification because of burnt contactor(s) inside the ignition switch.
What you can do is install a permanent resistor on the yellow wire in your ignition to trick the BCM. If done correctly your car should start every time after that. Okay now, let me be honest here: I've never done this myself, so if you decide to try this, I cannot garantee that it will work; but I've been reading many posts about this, and it appears to be workign for everyone who tried it... your call.
Check the following links; it is a discussion about this intermittent no start problem and that fix I'm talking about:
http://www.automotiveforums.com/vbulletin/showthread.php?t=731311
http://www.automotiveforums.com/vbulletin/showthread.php?t=698861&highlight=passlock+bypass
Hope this help