It is even better if your roast the chicken pieces, onions, celery, and carrots in the oven before you put them in the stock pot. It makes a darker stock as well. It is an extra step but you are rewarded with extra flavor.
Well, you hafta let it cool some so that the fat rises to the top, then you can use a ladle or large spoon to get it out by just letting the lip of the ladle submerge sp that only the fat and very little broth flows in.