Clearing the browsing history on Chrome for Android has always been a bit of a chore. You either had to memorize chrome://history, or bookmark it. Chrome 28 for Android has changed that by adding a menu item for quick and easy access to your browsing history.
To get to Chrome's browsing history on Android, hit the menu key, then select "History."
Once the history data comes up, you can click on the "X" next to the individual sites you want to clear. You can also click on the "Clear browsing data" button to clear your entire browsing history, cache, cookies and site data, saved passwords, and autofill data.