The Advanced Auto Logout Chrome extension is a handy extension for Chrome that makes your life easier by automatically quitting websites when you close your browser. In a few minutes, you can do the following:

Automatic logout from all websites that you want, including Facebook, Yahoo Mail, and all other websites that you have included. Automatic logout from certain websites that require two-factor authentication (e.g. google.com) 

In addition to that, you will have the ability to choose a list of sites that will be automatically logged out of upon closing the browser. For example, if you select Facebook, Yahoo, and Google, you will be automatically logged out of them when you close the browser. If you are logged into one website, it will stay logged in as long as you are not logged out of it. This gives you the ability to log out of websites that require two-factor authentication, without having to remember a second username or password. It is extremely useful if you use a shared computer or just want to enhance privacy.