Chrome can not do this by default, however its something that can easily be done with a plugin. You can do this by installing the History Limiter plugin from the Chrome Webstore. After the plugin has been installed you can configure it to remember your browsing history for 0 days. This will basically remember your history until you close Chrome at the end of your browsing session, after that your history will be forgotten however your cookies will remain so you can stay logged in to a website for example. Why not use Chrome's in private browsing mode? Doing it this way you can still stay logged in to websites if you wish, where as in private browsing will forget everything. It's also useful for website such as Facebook where you might authenticate each new device you access the website on. I personally use this method on my work PC as i don't really want to leave my internet history on there, however i also dont want to have to re authenticate myself on certain websites each day, or use in-private browsing. This solution works well for my needs anyway, hopefully you might find this simple, yet effective plugin useful too.