I think a reasonable approach would involve opening an iframe that talks to a dynamic page. The dynamic page would be auto-refreshed by two or more clients and continously post to/read from a table that stores the ID of the session, timestamp, user name(or IP), and message for the chats. The ID of the session would correspond to the dynamic page ID and bob's your uncle.
I'm sure there are various implementations floating around, but I'd want to control this on my own. No user accounts required if you set it up correctly, thought finding other users may be an issue without accounts.