If your website loads in Internet Explorer in IE 7 mode, the inline chat window won't work correctly, as IE7 does not support HTML5 (used by the inline chat window):
Try this line in your website header and then check in your IE (Press F12 to see the tools) to see how your page is loaded.:
<meta content='IE=edge, chrome=1' http-equiv='X-UA-Compatible'>
The X-UA-Compatible meta tag allows web authors to choose what version of Internet Explorer the page should be rendered as.
Here are your options:
"IE=edge" tells Internet Explorer to use the highest mode available to that version of IE.