Automatically sign out of Gmail when closing Chrome

1. On your computer, open Google Chrome.
2. In the top right, click the Menu .
3. Click Settings  Show advanced settings.
4. In the "Privacy" section, click Content settings.
5. Under "Cookies," click Manage exceptions.
6. Enter the site name you want to allow cookies for.
   • To allow cookies from an entire domain, insert [*.] before the domain name. For example,[*.]google.com. This creates an exception for mail.google.com, drive.google.com and calendar.google.com.
   • You can also put an IP address or a web address that doesn't begin with "http."
7. Use the menu to choose whether the site can set cookies. If you select Clear on exit, its cookies are deleted every time you close your browser and your mail session will end too.

You can also edit or remove exceptions using this box. Hover over the site or domain and click the , then clickDone.

thanks google help forum