Most likely you have flash Disabled, try enabling it
Type "chrome lugins" in the address bar to open the Plug-ins page.
On the Plug-ins page that appears, find the "Flash" listing.
To enable Adobe Flash Player, click the Enable link under its name.
To disable Adobe Flash Player completely, click the Disable link under its name.
IF that dosn't work
Youtube plays flash videos. usually chrome has built in flash. I would say either uninstall Chrome threw Start-Control Panel-Add/Remove Programs. And reinstall chrome. Or try to download flash player. http://get.adobe.com/flashplayer/