I cook mine for a long time, a couple of hours minimum, to get every last bit of flavor from the chicken. When it's time, I remove all the chicken and flavorings and then strain the stock into this nifty device which separates the fat from the broth. I use a fine mesh strainer and line it with a double layer of cheesecloth.
I am headed to Whole Foods tomorrow if I can stand the cold and get the provisions for 2 French Laundry recipes so y'all come back and check me next week.
See you soon.