1. change your "Live chat" menu item to NOT open chat in "New window"(it is not meant to work that way), if you desire users to open chat directly as detached window, we recommend you download and install "BlastChat WhoIsOnline" module and configure it to show "Direct popup/detach" link only (or adjust chat Configuration and set "Detached" to Yes)
2. Go to your website frontpage, login to your frontpage account, then enter chat - this will create new user in chat Administration so that you can set it as "SuperAdmin"
3. Remember, if you login to website.com and then you switch to
www.website.com, Joomla will not be able to keep your session and you will not be logged in. We recommend to set single access to your website using .htaccess rewrite rules as described here
How to create single domain access to your website