Steve,
I can't speak for the Milleneum stand, but my Screaming Eagle and Gorilla stands with chains are quiet once they are set. I prefer the chains over the ratchet straps because they make less noise when the temperature drops below zero.
If you are worried about the chain making noise while setting the stand, buy a can of the liquid rubber/plastic for coating pliers and wrench handles. You can get a can for 6-7 dollars at most any auto parts store and it will do a couple of chains. Dip your chain in the rubber/plastic, pull it out and let it dry for a few hours. It quiets the chain noise to almost nothing. Screaming Eagle offers it as an option on all their tree stands.
For larger trees, I carry several 3 foot sections of chain with universal links in my truck, in an Action Packer along with other Treestand hunting accessories. If there is a chance I will place a stand on a large tree I link an extra section of chain onto the stand before leaving to set it.