There’s no option for this, only clear cookies and cache until you quit the Chrome, but no history:
- Click the Chrome menu on the browser toolbar.
- Select Settings.
- Click Show advanced settings.
- In the “Privacy” section, click the Content settings button.
- In the “Cookies” section, mark “Keep cookies and site data by default until you quit your browser”.
- Save the changes.
There are some extensions that delete the history when you close Chrome, like this: