Melt the remaining butter over medium heat. Stir in the flour and cook for 1-2 minutes, or until bubbly. Slowly pour in the milk while continually whisking. Increase the heat to medium-high and whisk constantly until the milk mixture thickens to the consistency of thin gravy.
Add the thickened white sauce and prepared wild rice to the soup pot, stir, reduce the heat to medium low and simmer. Add the shredded chicken, adjust the seasoning if needed and enjoy!