Dain, great question! As of now we don't have this functionality built in. 

If you use your web browser's option to print the page you are viewing, and set the view to landscape, it is possible to print a snapshot of a brief part of a conversation if you are looking to capture all of it.

As far as fully exporting and printing a complete conversation, we do have an active request for this in our Feedback Center. We have added you to the request, which counts as a vote in it's favor and ensures you are updated on it's progress. Click Here for a guide to our Feedback Center