Earlier quoted context omitted.
We (Olark) specifically decided not to implement the "read-ahead" or "sneak-peak" feature because we thought it was creepy and broke customer expectations. When you are typing a message to customer service as a customer you should have a chance to compose your thoughts, and should have an expectation of privacy in whatever you are writing before hitting enter.
I like that a lot. It is creepy, imho. There's been more than a few times where I was up late, on a chat support, and quite upset about something or other... and decided to re-write my message before hitting the "Send" button. Composing your thoughts is valuable...
The point another poster made about secrets is a valid one but I'd argue that the kind of secrets you're likely to be pasting are the same ones the support operator would have access to anyway (payment details, address, order details, etc). But if you're really worried, other HN posters said it best when they commented about typing in a desktop text editor then paste your text into the chat window.