Some visitors can be rude and are not on the site for productive purposes. When that happens, simply use the blocking feature of your live chat tool.
What happens in most cases is that the visitor won't be able to see the chat widget anymore. When this is activated it's not possible for the user to start a new chat. It usually works with a cookie (a piece of data used by browsers) which will be stored on the visitor's computer and block them for a certain period of time (e.g. 30 days). Cookies can also be deleted, so if you have to deal with a tech-savvy visitor he might come back – but this hasn't happened to us so far. :-)