Combine all of the ingredients except the salt in a large stockpot. Cover partially and simmer over very low heat for about 1 hour and 30 minutes, skimming the surface of the stock as necessary.
Strain the stock into a large bowl and rinse out the pot; reserve the chicken for another use. Return the stock to the pot and boil over moderately high heat until reduced to 8 cups, 30 minutes longer. Season with salt.
The stock can be refrigerated for up to 3 days or frozen for up to 1 month.
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