Heat olive oil in a large pot over medium heat.
Add diced onion, carrots, and celery to the pot and sauté for 5-7 minutes until vegetables are softened.
Add minced garlic and cook for 1 minute until fragrant.
Pour in chicken broth and add dried thyme, dried parsley, salt, black pepper, and bay leaf.
Bring the soup to a boil, then reduce heat and simmer for 15 minutes.
Remove the bay leaf from the soup.
Add shredded cooked chicken to the pot and stir to combine.
Add spiralized zucchini noodles to the soup and cook for 2-3 minutes until just tender.
Remove the pot from heat.
Carefully ladle the soup into 4 clean mason jars, dividing the contents evenly.
Allow the soup jars to cool to room temperature before sealing with lids.
Store the soup jars in the refrigerator for up to 4 days.
To serve, reheat the soup in a pot over medium heat or microwave until hot.