To reply to a Live Chat, whilst the Chat window is open click in Reply field and type out your message:
Whilst you are entering this reply, the Customer will see a message on their browser stating that the Agent is replying:
The customer will then reply to you, and as they are doing this you will see a preview of what they are typing, so you can be ready as soon as they send the message with your reply, keeping the Live Chat efficient and professional for the customer: