In a large pot, heat olive oil over medium heat. Sauté onion, garlic, and celery until softened.
Add carrots and cook for another 2-3 minutes.
Stir in shredded chicken, chicken broth, half-and-half, thyme, and parsley. Bring to a gentle boil.
Add the gnocchi and cook for about 3-4 minutes, or until they float to the top.
Stir in chopped spinach and simmer for an additional 2-3 minutes.
Season with salt and pepper to taste before serving.