Perfect. Very simple:
//var ImageURL='<%= CuteChat.ChatWebUtility.HasReadyAgents()/*HasOnlineAgents()*/?URL_live_help_online_image:URL_live_help_offline_image %>';
//ImageURL= "<img title=\"support chat\" src=\""+ImageURL+"\" border=0>";
// write the live support button to the page
//document.write('<a href=\"###\" onclick=\"OpenLiveSupport()\">'+ImageURL+'</a>');
var ImageURL='<%= CuteChat.ChatWebUtility.HasReadyAgents()/*HasOnlineAgents()*/?"<a href=\"###\" onclick=\"OpenLiveSupport()\">LIVE CHAT</a>":"" %>';
document.write(ImageURL);