Clarifying Stock: making it clear and not cloudy
Hmm. Are you following the cardinal rules for stock making? 1. Do not stir! ever. 2. Skim, skim, skim. I add extra water initially so that I can skim the foam that rises to the top liberally. It's the reincorporation of the "impurities" into the stock that I believe makes it cloudy.
I strain twice -- once in a colander (after pulling out the chicken carcass and some of the veggies, and then a second time through cheesecloth over a sieve.
My thoughts are you are probably simmering on too high heat. The harder the boil, the more cloudy the stock becomes with impurities from my experience. Using the lowest flame possible and with no movement of the liquid in the pot always makes clear stock for me....and I do not use the normal egg whites and shells method either.
Stock should also be started in cold water, and as the previous posters have comments, cooked on a bare simmer, skimmed often, and never stirred. Blood will also cloud the stock so the bones must also be cleaned of blood and other matter (eg chicken insides) by rinsing and then blanching briefly. You can skip the blanching if you roast the bones prior to putting them in the pot.
Don't boil! Ever!
If you need to break up the carcass, get a good pair of kitchen shears and cut it up before it goes into the pot. And cut at the joints, not in the middle of the bone. And don't use the liver.
The easiest way to make perfectly clear stock is to make it in a slow cooker -- it avoids all the issues that cause cloudiness. Throw your chicken carcasses and your choice of veggies and aromatics in the slow cooker, cover with cold water, leave on low all day or overnight and you will have perfect stock. I learned this method on this board and have regularly blessed my fellow cooking hounds ever since.