How did you establish that the customer would have contacted you if not for webchat?

In the parent's scenario, it seems likely that the buyer for that enterprise was simply browsing through the site, or perhaps looking at various options, when they found the parent's site, saw that there was a chat and saw the near immediate response, asked a few questions and eventually set up a meeting. To do that over email would have likely taken days.

Source: I've had something like this happen too.

To answer your question, they told us directly in our first sales meeting (we didn't close the deal over live chat lol). The director we were speaking to said something along the lines of "and to think we probably wouldn't be here if I hadn't written you in chat."