For some time now I've been using IRC to connect to Twitch chat channels rather than using the Twitch chat in the browser and I can highly recommend it.
It has several advantages over the browser version:
connect to multiple channels at once and switch between them easily (handy if you're a moderator).
highlight text that contains certain keywords (customizable)
right click options (customizable)
buttons for mod actions (customizable)
system tray notifications on certain events (customizable)
last but not least, it's not in a browser :)
Rather than typing everything out and providing screenshots to illustrate the whole process, I went ahead and made a video (as you can see below).
IRC clients that work with Twitch and are easy to setup:
HexChat (used in the video): http://hexchat.github.io/
YChat (XChat2 for Windows): http://www.silverex.org/download/
Important: As of Sept 18 2013, you now require an OAuth token to connecto to twitch via IRC. I have created a desktop application that will generate Twitch chat tokens. You can download it here.