Heat the olive oil in a large pot, then cook the onion, carrots, and celery for about 5 minutes.
Stir in the garlic and cook for 30 seconds before adding the chicken breast.
Pour in the broth, then add the thyme, bay leaf, salt, and black pepper.
Bring the soup to a boil, reduce the heat, and simmer for 12 to 15 minutes until the chicken is cooked.
Remove and shred the chicken, discard the bay leaf, and return the meat to the pot.
Add the zucchini noodles and cook for only 2 to 3 minutes until just tender.