I do throw the skin and bones into making the broth. The chicken that I've found now isn't too fatty, so there wouldn't be much to skim anyways. But by all means, do skim if there is alot. Also into the pot I throw cut up celery and carrots, onion, garlic, 2 bay leaves, about 10 peppercorns and some natural no salt seasoning. I let this all simmer for a couple of hours, then drain.