How can I automatically clear my browsing data when I exit Chrome?

I don't like having my searches and web history hanging around forever. Therefore, I wonder: Is it possible to automatically clear browsing data on exit in Google Chrome? If it cannot be done with Chrome, do you know of any other good web browsers with this capability? P.S. I am not willing to root my device just for this purpose. Therefore, I'm looking for a solution which does not require root access.