How to disable Chrome's Incognito Mode?

To disable incognito on chrome/chromium you need to edit the policies. Doing this will prevent you from opening an incognito window via Ctrl+Shift+n, and will also grey out the incognito window option in the options tab in the corner.

If you're using chrome, create the folder /etc/opt/chrome/policies/managed. Or if you're using chromium, create the folder /etc/chromium/policies/managed.

Then create a file in that directory named test_policy.json. It can have any name you want, but it needs the extension to be .json.

Open it in your favorite editor and put:

{
    "IncognitoModeAvailability": 1
}

That should do it!

Source: http://www.chromium.org/administrators/linux-quick-start and http://www.chromium.org/administrators/policy-list-3

This doesn't directly answer your question, but rather than disabling incognito mode, you can instead enable the extension in incognito mode windows:

1. Click the spanner icon and then pick Tools -> Extensions from the menu.
2. Next to the extension you're interested in, click the expander arrow.
3. Check the "Allow in incognito" check box that is revealed.

Now the extension will be active in future incognito mode windows you open.

The caveat is that if the extension stores any information about your browsing history, your incognito browsing habits may not be as private as before. If the extension simply blocks certain URLs from loading though, this might not be a concern.