If I post a lovely animated SVG here, it will animate:
Beautiful, but the same does not happen in chat for me (Chrome, Mac OS):
This is a serious bug which needs fixing immedia-- ALL GLORY TO THE HYPNOTOAD
It seems that it's not an issue with chat playing the animation, because if you load a chat room with an animation it will play, but if posted while you're already in the room.
I assume the issue is that chat is not telling the browser to play the graphic when it is loaded.