On the guest side, the chat box offers a simple sound alert on each new message from the operator. You can opt to have the notification sound on or off by default on your chat boxes.
On the operator side, the answer all depends on which client you use to staff chat.
Webclient for staffing:
Pidgin and other external staffing clients
If you use Pidgin and our LibraryH3lp Pidgin plugin, you can configure the number of seconds for a looping audio alert for new chats. Pidgin users can also install the Guifications plugin for better visual alerting.
Users of other clients should look at their alert settings; these are usually quite flexible.