Separate chicken meat from skin and bones. *Reserve meat.
Bring broth and water to a simmer over high heat in a large soup pot. Add skin and bones to the simmering broth. Reduce heat to low, partially cover and simmer until bones release their flavor, 20 to 30 minutes.
Strain broth through a colander into a large container; reserve broth and discard skin and bones.
Return pot to burner set on medium-high and add oil, then onions, carrots and celery. Sauté until soft, about 8 to 10 minutes.
Add chicken and broth. Bring to a simmer. Add noodles and cook until tender.
(Soup base can be refrigerated up to 3 days in advance. Return to a simmer before adding noodles.)
Notes
*I always buy one of the big Costco or Sam’s Club rotisserie chickens. I use the dark meat for the soup and save most of the breast meat for making something like BBQ chicken sandwiches or chicken tacos.