In a Dutch oven or a large soup kettle, add the butter and onions. Saute for 4 to 5 minutes until the onions are starting to get tender.
Add the flour and stir in until well blended. Add your chicken broth stirring as you pour the broth in, once the broth is added pour in the milk stirring as it is added.
Add the celery, potatoes, mushrooms, chicken, bay leaf, and rosemary. Season with salt and pepper. Continue to cook until the celery and potatoes are tender.