Heat oil in a large pot over medium-high heat. Add celery, leeks, garlic; season with salt and pepper. Cook, stirring occasionally, until vegetables are soft, about 5 minutes.
Add the chicken broth, water, thyme, rosemary and bay leaf; bring to a boil. Reduce heat to medium-low and add the chicken and carrot noodles. Simmer for 3 to 5 minutes for al dente noodles, 7 to 9 minutes for tender.
Ladle the soup into bowls and serve, garnished with parsley. Serve alongside crusty bread, if desired.
