In a large pot over medium heat, melt butter.
Add celery, carrots, onion, and garlic, and saute until tender, about 8 minutes.
When vegetables are tender, stir in flour. Allow flour to heat through, about 2 minutes.
Slowly add the chicken broth while stirring to prevent lumps.
Add chicken and bring mixture to a boil.
Add gnocchi, and cook until done, about 5 minutes (check package instructions for precise time).
Lower heat to medium-low. Add cream, and stir to combine. Heat to steaming, but not boiling.
Stir in spinach, thyme, and salt and pepper to taste. Allow spinach to wilt and soup to totally cook through.