There are times that chains are required to be able to drive on the freeways and even just city streets when the weather gets horrible in Portland and the outlying areas, to have to park the tahoe because Chevy or GMC says not to and not knowing why just doesn't sit well with me!!
What I do with every truck that I get a new set of chains for is dry fit them on the truck with it jacked up in the air, I fit them perfectly without slack in a perfect world environment (not on a snow covered road with the tires on the ground), I count the links dangling on the inside and the outside and make sure it is a perfect fit, I spin the tires and make sure nothing is in the way of them (like a brake line or fenders), even turn the steering wheel full left and right, both times spinning the tires making sure nothing is hitting anything. Next undo the chains and put the truck on the ground, now it is time to do it all over again but in a real world environment, run over the chains and try to get the same number of links dangling like when it was off the ground, you should be able to get within a link if not the same as it was off the ground, if not keep messing with them until you take up the slack. Once you get them the way they need to be, take them back off and the links that would be dangling on the inside and outside of the tire get some bailing wire and wire tie them to the chains where they won't stick out or be in the way at all, if real world application get you within one link, that would be how I would wire tie them( I like bailing wire instead of zip ties because more than likely you will only use that set for that truck and the wire seems to last forever unlike the ziptie), you should be able to take up the little bit of slack with the rubber tensioners you put on the outside of your tire. Cool thing about doing this is even if you don't use them for years it will be obvious how you are suppose to hook them up.
Last but not least, give it a road test, preferrably in snow, and check driving straight and turning, often times you won't encounter a problem until you get up in speed so keep your ears open for any signs of trouble.
Also, call up a service dept. at a Chevy or GMC dealership and ask them why your book would tell you not too use chains, I find that crazy except in the instance of fender clearance or brake lines being in the way, which if you set your chains up in this manner and check it you shouldn't have a problem. If is a matter of drivetrain having more grip in the front with the chains but not having chains for the back(maybe in an all wheel application), buy 2 sets, front and back (you will be an unstoppable tank for sure!!).