After running CCleaner, Chrome's history *appears* to be deleted, but typing in the URL bar elicits auto-completion suggestions of websites I visited before the cleaning. So, there is a history file that CCleaner is not deleting. I can fix this problem by manually clearing my browsing history in Chrome, but this is what I have CCleaner for.
I haven't enabled syncing, so I don't believe these suggestions are coming from online.
Nothing constructive to add I'm afraid. Just to say that with Chrome, if you suffer a crash for whatever reason and close the browser and perform a thorough clean, then when the browser is reopened it will politely remind you of the crash and offer to reopen your last page. Obviously quite a lot of information is being retained.