In a large pot or dutch oven, melt coconut oil over medium high heat.
Add onion, carrots, celery and salt. Stir and cook for about 8 to 10 minutes.
Pour in the bone broth, and add thyme, basil, and bay leaf. Bring to a boil, then reduce heat and simmer for 10 minutes. Add pepper to taste.
While the soup is simmering, prepare the zoodles by peeling the zucchini to remove the green skin. You can leave it on if you like. Peeling makes them look and feel more like regular noodles. Run the zucchini through a spiralizer or use a mandoline set to cut julienne. If you use the spiralizer, you may want to roughly chop through the pile of zoodles to make them shorter and easier to eat in your soup. Set aside.
When the vegetables have softened, add the diced chicken and zoodles to the soup and cook for an additional 10 minutes.