Thanks for the possible solutions.
Regarding the first step, I know that my Chrome sync is only set for Bookmarks, Extensions and Settings. I double-checked just now and as I thought, History is definitely not selected.
"Continue running background apps when Google Chrome is closed" was selected, so I disabled it, closed Chrome and ran CCleaner again. History remains. I did also check that no chrome.exe instances were running under Process Explorer, and there were none.
I'm thinking something has changed in the latest Chrome Beta as this has only arisen since the latest update.