Into a blender or food processor add the artichoke hearts, egg, white wine and blend until smooth. Set aside.
In a large saucepan over medium heat melt butter. Mix in flour, salt, and pepper stirring until well combined and lightly golden brown. Slowly add cream and milk, whisking until mixture begins to boil and thicken.
Turn heat down and gradually add artichoke puree and chicken broth, stir well. Heat the soup adding more salt and pepper if needed. Serve hot with a dab of sour cream and chopped chives as a garnish.