This extension enforce Chrome/Chromium to always use the Incognito mode.
How to use it:
Simply add it to Chrome.
To disable it:
You can click on the extension icon via the Settings or disable completely the extension in chrome://extensions.
Some tips: I recommend to clear all browsing data before using it and use reasonably bookmarks to replace history. You may want to enable your installed extensions when using Incognito, you can do it by navigating to chrome://extensions. Remember that in private mode, everything you do (except downloads and favorites) are not saved so every time you close the browser, pouf, it's all gone. I've been doing this for years and I can perfectly use a browser without history of anything so you should try it, I bet you will love it too. Other extensions that goes well with this one are: uBlock Origin, HTTPS Everywhere and 1Password.
Note: This extension cannot be enabled in Incognito mode for obvious reasons.
Thanks to Jems Mayor for the original icon.