In a large pot or Dutch oven, heat the olive oil over medium-high heat. Add the celery, onion, and carrots. Saute for 2-3 minutes or until veggies start to soften. Add the garlic and cook for 30 seconds.
Add the chicken broth, chicken, and thyme. Bring mixture to a boil and add the gnocchi. Reduce heat to a medium simmer and cook gnocchi for about 8-10 minutes or until tender.
Stir in the half and half and spinach. Simmer for 2-3 minutes or until spinach is wilted. Add salt and pepper to taste. Soup will thicken as it sits.