In a large stockpot, melt ghee over medium heat. Add onion and celery, cook for about 5 minutes or until the onion becomes translucent.
Add chicken broth, water, chicken, basil, oregano, parsley, salt, and pepper. Bring to a boil, then reduce heat to low-medium, cover, and simmer for 10 minutes.
Using a spiralizer, cut chayote squash into noodle shapes. Once the soup has simmered for 10 minutes, remove the lid and add in chayote noodles. Simmer without the lid for an additional 10 minutes. Remove from heat and serve.