There is currently no “pin” feature in Discourse chat. There should be a pin feature for the chat, in case important messages need to be pinned for users to read. Pinning messages can be done if you are a moderator/admin or if you are in a personal message. This feature is currently implemented in Discord, as can be seen below:
Seeing that screenshot makes me wonder if we could merge pinned messages into the same panel we use for chat threads.