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Add chicken, carrots, celery, and onion to a large stock pot. Cover with water. Bring to a simmer over medium/high heat. Cover and simmer over medium heat for 35-40 minutes. Check every ten minutes, and skim off any fat/foam that forms at the top.
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Carefully remove the chicken from the pot. Place on a cutting board to cool while the soup keeps simmering for ten minutes. After ten minutes, use a knife and fork to remove the skin from the chicken and break the meat up into large chunks. Discard the skin and add the chicken pieces back to the pot.
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Add the egg noodles and simmer over medium/low for 7-10 minutes until they are done. Remove from heat. Let cool for ten minutes before serving. Chicken noodle soup will last in an airtight container in the refrigerator for a week and half. It will last, stored in the freezer for a month.