Prevent multiple chats from same user

We would like to be able to prevent the same external user (customer) from having multiple chats open simultaneously, to avoid confusion for both the user and our reps. With cookies disabled, this could also lead to duplicate credits by different reps unknowingly chatting with the same customer. We could disable the button on our website when they launch a chat, but we'd have know way to re-enable it when the chat closes.