How to force only Chrome to send network traffic through VPN connection on Windows 7?

I think, for what you want to do, you can use the Proxy Switchy! extension for Chrome and create a different profile for your VPN and set the Network in the Proxy Switchy! settings as so:

This seems to be the easiest way to achieve what you want as selecting a profile will route through that specific connection.

All your other traffic will be routed through whatever the local connection is, and your Chrome traffic will be routed through the VPN.

Actually, with windows 7, this is easy with windows built in firewall. This link gives a very easy description of the necessary steps. http://practicalrambler.blogspot.com/2011/01/windows-7-firewall-how-to-always-use.html

Basically, make an inbound and an outbound rule blocking traffic of private and domain networks for the program you want to isolate. Be sure to NOT block public traffic with the rules. This also requires that your VPN is setup as a public network and your LAN is setup as private....

Set up chrome to use the VPN as a proxy.