Ability to upload CC/subtitle files
The ability to have closed captioned and subtitled videos. Twitch wouldn't need to have a closed captioning system, just the option to upload a CC file (i.e SubRip, SubViewer, RealText, etc) and preferably to be able to maintain the more advanced files' caption positioning.
You could output the CCs into chat on client-side (extra tab or interfering with other chat messages, or for the user to enable/disable CC and people) as a fast, cheap first approach.
Nathan S. commented
I totally agree!