The normal chat system is done using the XMPP protocol.
Recently, Riot released a new way to communicate with other people within the game. They called their new system the "Clubs" (btw we have a SEN club). Guide to Clubs
It's similar to the normal chat rooms except that when you log back in, you can see a certain amount of messages that you missed while being offline.
It seems like the LoL client connects to http://clubs.leagueoflegends.com:443
I'm trying to get my own program to be able to connect to my league account in order to talk in a club.