Virtualbox access issue

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 you just used the default Network settings in your VM, it will be NAT with DHCP. That means you get a LAN IP from your VirtualBox DHCP Server and you can't really access the machine from the outside.

Check out the VirtualBox Manual on Networking: https://www.virtualbox.org/manual/ch06.html#networkingmodes

I guess bridged neworking should be best. You should configure a static IP address.

EDIT: Concerning the edit removing "host-only networking": It's true that you can't see the VM from outside. But you get virtual interfaces (vboxnetX) on your host machine. So if you route it through, it should work. The setup is more complicated, but the VM is less exposed.