This feature has been requested many times at Chromebook Central and probably many other places and the answer in the past has always been to create a solo session of Google 'Hangouts On Air'.

Now, with the help of Googler Francois Beaufort and his How-To, it can be done via 'crouton'.

Check it out:

If you'd like to use a slightly modified version of 'screencast.sh' with some command line options added, checkout 'screencast'.

To obtain the file 'screencast', in a cros shell (crosh) do:

curl -Lk --connect-timeout 60 -m 300 --retry 2 "https://gist.github.com/DennisLfromGA/8441689/download" | tar -xzO > ~/Downloads/screencast