Make sure you are allowing pop ups from Chess.com as the email should come up in a new window. If you are still having problems try using this link - https://mail.chess.com/parse.php?file=html/english/xul/xullogin.html&XUL=1
email problems
Tried your link I had an option to allow pop ups from this site and selected it but it still comes up with the same message. 
I've had a look at this and can see what you mean. Until i can get this fixed for you, when you open emails and that error message appears, click on the left side where it says "inbox" and your emails should then appear for you.
Further to the problems loading up the email facility using firefox, I attempted to move to google chrome and it is even worse and won't load at all just gives a message at the bottom mentioning the word "parse" I believe. Sorry for the little amount of detail. At work at the moment using internet explorer and it works fine there.
I haven't tried using the chess.com email facility for ages. I have moved over to mozilla firefox recently and now when I try to get into it I get the following "
Not Found
The requested URL /https:/mail.chess.com/util.php was not found on this server."
can anyone help so I can access without having to go back to internet explorer?