Right now, you can drag messages to the chatbox to quote them (drag the arrow box that shows up on hover on messages to give the the message options context menu). You can also click the show all link in the starred feed to get real messages and drag those as well.
Is there a way to drag starred feed messages from the starred column in the same chat window.
This works because the message arrow context menu acts as a link. Can the starred columns message arrow context menu do the same?