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Today I was in queue for Normal Draft SR, and during bans/champion select, chat was not functioning. I was able to write out messages, however, on sending, the message would disappear from the input field and nothing would appear in the chat window. My teammate's chat messages would also not appear. I dodged and exited the client, so I'm not sure if the game itself would have maintained this bug too.
The only thing out of the ordinary I can think of: While in queue, I moved from a wireless to wired connection, and in doing so, lost connectivity for a moment. PVP.Net reported a disconnect, but I reconnected and stayed in queue--I was able to access my friend list so I assume I was properly connected.
I believe I was still able to send and receive messages--the "message sent" sound played, and I heard some messages sent from my teammates, so it was possibly just a display glitch.
I don't have much of an idea for reproduction, but I suspect the changes made to my connectivity were involved:
 Enter SR > Normal > Draft queue on a wireless connection [home network, Belkin router, cable connection, if relevant]
 While in queue, connect to the same router via ethernet [on Windows 7, this means being connected via both wireless and wired]
 Disable the wireless connection
 Notice PVP.Net's disconnect notification, but stay in queue
 After match is found, enter champion select and try to chat