Do not throw away chicken carcasses!
Any time you eat a whole chicken keep the skin and bones.
Last night we had two roasted chickens. I kept the seasoning simple just rosemary from the yard, garlic, salt, and pepper. When we were done eating dinner we picked the bones free of the meat. Tossed all the bones in a large pot. I don't like to eat the super fatty skin pieces, they are too squishy for me, so in the pot they went too. Fill the pot with water and two bay leaves. Simmer on low for 12-18 hours. If I have leftover celery tops or carrot pieces I'll toss them in towards the last few hours but they are not necessary.
Strain out the solids and let cool. I freeze all but one jar (if it's glass freeze it without a lid) and use it wherever chicken stock is called for. The long cooking time yields a super tasty soup base. The longer you cook it the thicker the liquid becomes. If it appears gelatinous when cooled don't fret. Just heat and add water. Think of it like goodness concentrated.
The only warning in using homemade chicken stock is to watch the salt. You salted the original chicken so your stock will have some salt in it. If you use the stock in a recipe test the saltiness of the dish before adding any more.