This raises an interesting point: Skype downloads your chat log from their server. They have your chat log on their server.
http://blogs.skype.com/2013/10/04/skype-architecture-update/
http://www.makeuseof.com/tag/skype-enables-synchronization-o...
Anyone who thinks the NSA can't reach MS is unaware how easy it is to turn people. The KGB turned FBI/CIA agents for years, for paltry sums. Said spies claimed their only motivation was money. The USG would be incompetent if they didn't have agents working for all sorts of companies.
Between all their resources, it's possible the NSA has setup some way to copy all Skype messages.
But I would be very surprised if Skype was knowingly sending all data to them voluntarily. MS has denied this, and it'd require a lot of people to be in on it.