Add chicken, wild rice, onion, carrots, celery, garlic, chicken broth, salt, pepper, and thyme to a slow cooker.
Cover and cook on low for 6 to 8 hours, or on high for 4 to 5 hours, until the chicken is cooked through and rice is tender.
Remove the chicken, shred it, then return it to the slow cooker.
In a small saucepan, melt butter over medium heat. Whisk in flour until smooth, then slowly add heavy cream while whisking continuously to form a roux.
Stir the roux into the soup and cook on high for an additional 15–20 minutes until thickened.
Serve warm and enjoy!