If you are simply streaming a stored video, you can just get the file size, use that as the content-length, and send the video. If the content is in a streamable format the client can just read/play the data as it is received. Chunked encoding will in fact add a little overhead to just sending as is.
Chunked encoding is more apt for situations where you don't know beforehand how much data you are going to send.
What they do is parallel-encode their video feed to many different bitrates, then as the client is keeping up or not keeping up with the incoming chunks they move up or down the scale of which chunks to send. The best part is, it works via existing http cdn's like level3 and akamai, so just about anybody can stream live video this way to as many people on the internet as they can get to watch it for the already commodity cost of cdn bandwidth.
[1] - http://arstechnica.com/apple/news/2011/04/adobe-throws-in-to...
See:
http://tools.ietf.org/html/draft-pantos-http-live-streaming-...