Same happens in older Webroot and AVG, and Kaspersky can be a pain too. Just disable the anti-virus when you clean- or configure it to accept CCleaner access to private/personal folders.
The worst case would be uninstalll the Anti-Virus, run CCleaner, re-install Anti-virus and hopefully its' automatic program permissions will pick on CCleaner being legit- what I did with Kaspersky 2009, 2010, 2011- till I changed Antivirus.