Thanks for the acknowledgement ParisPete. I'm glad it works for you.
I haven't stated my actual opinion for a while. Chess.com should sign their java applet and none of this discussion would be necessary. It is not a difficult thing to do http://stackoverflow.com/questions/19542225/sign-java-applet-for-work-without-java-warnings. There is a cost but it isn't high for a site like chess.com (I found prices for $200 to $500 per year via a quick web search).
Earlier in this thread someone said that all resources are being applied to a site version 3 which won't use java. I understand that as a long term strategy but I think they should also sign the applet now.
That said, it does work for me now and I'm not thinking about cancelling my membership.
It works!
I'm running XP with service pack 3 using Google Chrome.
Go to: Control panel -> Java -> Security -> Edit site list -> Add http://cssjs.chesscomfiles.com/ OK OK
Accept the risk when asked.
Voila!!! Thanks to brmchess.
ParisPete