There is a Pastafarianism Chat room that was created as a child of English.SE. As this is chat room for an Area51 proposal it the room should probably be a child of Area51.
I searched and found two somewhat related question Unwanted feature: chat account auto-re-parenting & What happens to chat rooms whose parent sites get closed? neither seems to address this question.
The URL is not parent specific, so it would seem parent is an attribute that should be easy to change. Can a chat room have the parent site (also known as host) changed?