At this time, Google Chromebook has very limited native VPN support.  We have had some customers report success using IPSec however we highly suggest OpenVPN for security reasons.  At this time OpenVPN is not fully compatible with Google Chromebook at the ChromeOS level.

Newer models of Chromebooks support Android apps via the Google Play store.  The IVPN App for Android works very well on these newer Chromebooks and can be installed just like any other app.

In some cases, the Android subsystem and the ChromeOS subsystem are not 100% in alignment and it may be the case that the default ChromeOS web browser does not make use of the VPN tunnel.  You might consider installing an additional web browser from the Google Play store to take full advantage of the VPN connection.