Facebook, and it's launched a "Ticket Window" to allow users to do just that. This is apparently just the first of many Ticket Windows, which the company also plans on installing in banner ads, making it the first airline to move in this direction. Presumably the draw here will be to streamline the booking process, making it easier for Delta customers to book their flights. Delta, which is the largest commercial airline in the world is facing ever-increasing and savvy competition from smaller, more web-friendly airlines like Virgin and Jet Blue. It's unclear when the Facebook ticketing will begin, but for now, it's fair to say that, at least in theory, we "like" this.
Updated: The company that developed the app, Alvenda, has informed us that it is, in fact, live on Facebook now -- so go start booking flights!