Chrome for iOS received an update on Wednesday with tighter integration of Google's other apps. The update also included access to browsing history, which had previously been unavailable to iOS users. Android users have had access to browsing history for some time now, but with Chrome 28, iOS users get it too.
To access browsing history on Chrome for iOS, tap on the Chrome menu, then select "History."
You can remove individual Web sites from history by tapping the "X" next to the entry.
If you want to remove all browsing history, tap on the "Clear Browsing Data" button at the bottom of the history list. This will bring up the Chrome privacy options, which also allows you to clear cache, cookies, site data, passwords, and bookmarks.