One of the reasons so many car shoppers use chat to contact a dealership is the fact that chat is discreet - that is, chat allows them to communicate with the dealership without drawing attention to themselves. 

Looking at dealer weblogs one can quickly see that many shoppers do their browsing while at work.  It follows that, when at work, people are hesistant to call the dealership or be called because a phone call will likely draw attention and expose the fact that one is car shopping instead of working. 

Chat, on the otherhand, is just as discreet as browsing.  A shopper can get their questions answered and schedule a test drive appointment without drawing any attention to themselves.  Check out the following chat conversation transcript which is an actual conversation. 

Key tip - It never hurts to ask for a phone number but don’t be surprised if shoppers contacting you via chat are at work and unable to get on the phone.  Go ahead and close on the appointment or appropriate next step via chat.

Actual Dealer Chat Transcript