yes, Yes, YES!!! Mine (1500 Z71, though) did this too when it was brand new--right after we bought it. (We bought it in October, so there were plenty of cold morning starts.) I took it in to the dealer, and they replaced the serpentine belt. It still did it for a day or two after they replaced it, but I haven't heard it since. I don't know if there was a true TSB or somesuch on this, or if I had some dealer perogative thingy... But the replacement seemed to be much better. We'll see when it gets cold agian.
BTW, to further characterize the problem, the chirping was loudest at idle or slow speed, but had a definite frequency loop. That is, it's as if it was specific to a certain portion of the belt and would get louder when that part of the belt came 'round again. The faster you drove (and hence the faster the engine speed), the chirp "oscillation" would go faster and faster until you couldn't really make it out from the other truck noises... Hope this helps. The original belt looked fine too.