We are working on this feature right now! It should be available soon.

In the meantime, you can save a chat by converting it into an email and sending it to yourself. Here’s how:

1. Finish your chat. Then, before you close the chat tab, click the envelope icon in the upper-right corner. It’s one of three buttons above the chat window, to the right. See it? Click it to convert your chat to an email.
2. Look, your chat is now an email with a blank "To:" field. Send it to yourself by typing your own email address after "To:". When you receive it, file it in whatever folder you want.