How do I keep Google Chrome from blocking Java because it is out of date?

The "right" way to fix it is by updating Java. However, there are always cases where for one reason or another, a user is not able to install software or perhaps specifically cannot update Java.

Google allows for a workaround, though they don't really recommend it. Here is their answer:

You just have to add --allow-outdated-plugins to your command line and it will prevent you from seeing the message. A word of warning though, this disables the check for ALL plugins, not just Java.