Live chat uses a plug-in for your web browser that runs a programming language called Java. It's pre-bundled with most browsers these days (Internet Explorer, Firefox, Safari, etc.), but for some reason it appears that either you don't have the Java plug-in installed, or it's simply failing to load (hence the big red "X").
There's a couple things you could do:
1. Make sure you've got the latest version of your web browser running, and that your computer is completely up to date with the latest patches, system updates, etc. If Java is missing, your computer should notice, and prompt you to install the update. If you've got a techno-genius for a friend/relative, you might want to ask them for assistance. Tell them that web sites which use Java plug-ins aren't working for you. It's also possible that "Internet Security" software or anti-virus software on your computer is preventing Java from running.
2. Ignore it (for now). I've yet to see anyone using the "Live Chat" feature, so I doubt you're missing much. I think most people are exchanging Instant Messaging IDs, and going from there.
There are other things online which also uses Java, so if you keep running into those big "X" symbols, you'll eventually want to get that fixed. However, good 95% of stuff online will work as you currently stand.