Configure VirtualBox to connect to Internet through proxy

This isn't a VirtualBox (or Windows XP) problem - you need to instruct Chrome OS to use a proxy. The virtual adapter in VirtualBox can be configured to Bridged or NAT, though NAT would probably simplify your life somewhat.

I don't have a Chrome OS VM - so this part is just a guess based on my Chrome browser, but can you click on the wrench icon -> Options -> Under The Hood (tab) -> The under the network section, click the "change proxy settings" button?

There may also be a way to export the right environment variables (http_proxy most likley) in your startup scripts, as Chrome OS shares a certain legacy with Linux and Ubuntu, but I can't comment specifically on it.

Side Note: Your VirtualBox version is a bit out-dated, have you considered upgrading?

If your virtualbox network adapter is set to NAT at the moment, try setting it to "bridged" and make sure your host OS has made a connection through the proxy to the internet before launching the virtual Chrome.