Live Chats can be assigned a Department and Queue, and this can affect what Agents can view a Live Chat.
Support Agents for instance might be configured to only view Support Live Chats.
Typically Departments will be set on Live Chats via workflows when they are created, but its possible an Agent will claim a Live Chat and find it is actually in the wrong Department.
This could mean that this Live Chat needs to be picked up by another Agent who can handle this Live Chat subject, or it might be that the current Agent can still deal with the Live Chat, but from a reporting point of view this should still be set to the correct Department and Queue.
In order to transfer a Live Chat to a different Department and Queue, on the left information panel on the Live Chat there is a section for the Department and Queue:
Clicking on the Move option against the Department gives you a prompt to determine the Department and Queue you want this Live Chat to be set to:
Once you have confirmed the new Department and Queue this Live Chat will be updated to display this new Department and Queue in the information panel on the left: