In a large saucepan, heat the butter over high heat until melted. Add in the carrots, celery, onion, thyme, salt, pepper and bay leaves. Cook for around 5 minutes, or until onions are translucent.
Mix in the chicken broth and rice, and cook for around 25 minutes. Add in the chicken and cook for around 5 minutes.
Meanwhile, in a medium bowl, mix together the whipping cream, milk and flour. Mix into the soup and cook until the soup is thickened. Serve immediately.