Spiralize zucchini using the medium blade (not the very smallest one). Set aside.
Heat oil in a large pot over medium heat. Cook onion until tender. Add chicken (if raw) and cook until browned, about 5 minutes.
Add broth, poultry seasoning, basil, carrot, and celery. Let simmer uncovered about 15-20 minutes or until vegetables are tender.
Stir in zucchini noodles and let cook 1-2 minutes or just until slightly softened. For firmer noodles, place raw noodles in bowls and ladle hot soup over zucchini noodles. Allow to sit 2 minutes to soften.