I am using Google Chrome.
I tried HTML5, pepper flash, and normal flash but I always see the video on one monitor.
http://www.youtube.com/v/[video-id] but I see the Chrome tabs and bars.
Do you have any idea?
So long as your OS sees your monitors as two, distinct screens I don't think a browser plugin will be able to (effectively) split the video and project the separate halves on separate screens in sync.
What OS and video card are you using? Display adapters like the Matrox DualHead2Go Digital or the AMD Eyefinity will create a single display from your multiple screens. Then, when your video goes full screen, it will spread out across multiple monitors as you intend.
The adapter needs to be comparable with the graphics card, so you'd have a bit of homework to do.