You can try using the following nifty program to see where Chrome tries to install your specific extension: Sandboxie
(Note that it's not free so there's a 30 day trial limit)
To see where Chrome installs the extension you will need to first run Chrome inside Sandboxie which will trap the specific instance of Chrome in a sandbox. What this means is that whenever Chrome tries to make a change to the system for example deleting a file, the action happens on a replica of the file in question and not the original. In the case of creating a file, the file is created in the sandbox and Sandboxie can easily reveal only new files created or modified by Chrome.
Once it's running create a new profile and add the extension you are looking for to it. After the extension has been installed you can safely close Chrome.
Next you need to inspect the contents of the Sandbox to see where Chrome created the extension. Once you have figured out the path, you can grab it from the non sandboxed path.
There's a simple guide on their site which explains the steps in more detail.