Peel and dice potatoes into 1-inch cubes and place them into a large crock-pot. Add in diced celery and onion. Pour in chicken broth, cover crock-pot with lid and cook on low heat for 6 hours, or on high heat for 3-4 hours.
In a medium saucepan over medium heat, melt butter. Add in flour and cook for a minute to brown. Whisk in milk and sour cream, let cook over medium heat while whisking constantly until sauce has thickened.
Pour the sauce into the crock-pot, cover and let cook for another 30 minutes. Blend soup with an immersion blender or blend soup in batches until smooth.
