Rinse wild rice in cold, running water and drain well. Place in the crockpot.
Season chicken with salt and pepper to taste. Place in the crockpot over rice.
Add onions, carrots, and celery.
Add chicken broth.
Cover and cook on HIGH for about 3 to 4 hours or on LOW for 7 to 8 hours.
In a saucepan over medium heat, heat butter until melted. Add flour and whisk into a smooth paste. Continue to cook for about 1 minute or until lightly browned.
Gently add milk, whisking vigorously to prevent lumps, for about 3 to 5 minutes or until slightly thickened.
Remove chicken from pot and shred using two forks. Return shredded chicken to slow cooker.
Slowly add milk mixture, stirring to combine, and continue to cook for about 2 to 3 minutes or until chicken is heated through and soup is thickened to desired consistency.
Season with salt and pepper to taste. Serve hot.