Chromium can definitely play H.264 with no problem. All three videos on this page[0] play perfectly, as do all other HTML5 YouTube videos.[1]

[0]http://ie.microsoft.com/testdrive/graphics/videoformatsuppor... [1]https://www.youtube.com/html5 - This shows 6/6

I'm a bit shocked that this works even on Debian. I don't understand how it is possible without Debian violating the patents.

Chromium uses ffmpeg to decode h264. In fact, they even include ffmepg in the chromium source tarball.