I was logged in to sync my bookmarks. However, I discovered that under Advanced Sync Settings, in Chrome, I had History checked. You can remain logged in and ccleaner WILL clear your history IF you have History un-checked in the Advanced Sync Settings. Thanks for the clue!
The clear history on the version 38.0.2125.104 m of the Chrome browser on Windows 7 Home Premium (64bit) does NOT get cleared by running ccleaner version 4.18.4844 (64 bit). The only way to clear it is with Chrome's own clear feature. This is with all instances of the Chrome browser closed and then running ccleaner. The program indicates that it deleted/cleaned xx number of history files but when you start Chrome after cleaning and check the history, they are ALL still there. Only Chromes internal clear function currently works.