No, you don't have to let visitors and contacts chat (but we think it's pretty cool).
You can disable the chat feature but still allow for contact notifications when visitors arrive.
Chat settings can be enabled or disabled, per button. Start by heading over to the buttons screen. You will then want to select 'Visitor Buttons' and then click "edit" on the button you would like to edit chat options for. Scroll ALL the way to the very bottom where you can turn on or off 'two way chat.' Don't forget to save!