You can host HipChat Private server as long as you can bring it up using the formats provided (ova and ami). Not though that you'll still be using a couple of cloud services (the push notifications and video). Your best bet might be to ping firstname.lastname@example.org with the specific concerns.
In addition to Daniel's answer, you should have issues to install HipChat server over VPN.
If you need to use install HipChat in another network / hosting (such as Amazon), the VPN is the best option (you have many possibilities (like enable BGP) depending of what firewall/VPNserver you are using).
Otherwise, if you are planning to setup this between your offices you can setup this without a VPN software using MPLS connection, fibre channel (it depends of your infrastructure).
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