Heat oil in a large soup pan or Dutch oven over medium heat. Saute the onions and celery (stirring frequently) until onions are softened and translucent (about 7 minutes).
Add chicken, kale, squash, broth, water and herbs and stir to combine. Bring to a boil, add barley, stir and reduce to a simmer.
Cover and cook for 50 minutes or until barley is tender.