Quote: "think of the chances."
Actually pretty bad. The Yahoo! chatrooms have been, for quite a while, constantly infested with pedophiles - many pedophile rings that have been assimilated used Yahoo! primarily, in fact. Because they simply don't moderate at all. Two recent measures, requiring a valid credit card to create an account and shutting down user created rooms, may have helped somewhat, but it was always the Yahoo-created regional rooms that were the biggest problem anyway, and they're still not even slightly moderated.
At the end of the day parents need to watch everything their kids do online. Still, that doesn't void webmasters from an incentive to keep their place safe. So XpProUser, I would simply recommend you appoint several moderators you trust to the chatroom.