With live chat software, not only can you offer chats on demand, but it's also possible for you to initiate them.
There are two different possibilities:
Set an automatic trigger to start the chat – e.g. after your visitor has spent 2 minutes on your site or if they surf to a specific page (that has sales relevance for example)
Manually start a chat with visitors whose profile looks interesting according to your analytics (not all live chat tools offer this feature)