In a large pot or dutch oven, melt the butter over medium heat.
Add the onion and celery. Saute until the vegetables are soft, about 3-5 minutes.
Sprinkle the flour over the vegetables and stir quickly.
Slowly whisk in about 1 cup of the broth. Be sure that the flour is full combined and not clumpy - whisk continuously.
Add the remaining broth, wine, salt, pepper and thyme.
Bring the soup to a boil, stirring on occasion.
Stir in the vegetables, chicken and cream (or half & half).
Serve warm with pie crust crackers.