Customer one-on-one private chat possible?

Hi,

is there a possibility to use chat (or any of your plugins) to engage into a one-on-one chat session with a website visitor? Also it would be great if the visitor can start this chat on his end.

I have gone through "Chat" PlugIn but am unable to configure it to work this way. If possible please send me details of the configuration necessary.

It is vital the the session is ONE-ON-ONE to give individual support and full disclosure.

Thanks.