Just to note this here as it seems this hasn't been mentioned yet, the Twitch chat is based on IRC. They run their own servers and you have to log in with your Twitch credentials but you can user your usual IRC client to connect to the Twitch IRC.
In addition, special Twitch IRC clients have spawned, like TC [1] or Chatty [2] that include support for Twitch-specifics like Emotes, notifications and direct linking to the associated video streams.
In addition, special Twitch IRC clients have spawned, like TC [1] or Chatty [2] that include support for Twitch-specifics like Emotes, notifications and direct linking to the associated video streams.
[1] https://gettc.xyz/
[2] http://chatty.github.io/