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 the chicken broth and bring the mixture to a boil.
Reduce heat to low and add shredded chicken, dried thyme, dried parsley, salt, and black pepper.
Simmer the soup for 15 minutes to allow flavors to meld.
Remove the pot from heat and let the soup cool slightly for 5 minutes.
Divide the spiralized zucchini noodles evenly among the 4 mason jars.
Ladle the hot soup evenly over the zucchini noodles in each jar, leaving about 1 inch of headspace at the top.
Seal the jars tightly with their lids and allow them to cool to room temperature before refrigerating.
Store the jars in the refrigerator for up to 4 days.
To serve, heat the soup jar in the microwave or pour into a pot and warm on the stove until hot, allowing the zucchini noodles to soften.