At Microsoft's 2014 build developer conference, Frank Savage, Partner Development Manager at Microsoft, revealed that they have plans for an Xbox 360 emulator.
He revealed this during a Q&A after the “Understanding the Xbox One Game Platform Built on Windows” session:
Q. Are there any plans for an emulator for the 360 games?
A. There are. But we aren’t done thinking them through yet unfortunately. It turns out to be hard to emulate the PowerPC stuff on the x86 stuff. So there’s nothing to announce, but I’d love to see it myself too.
So we could be waiting for a while, but it sounds as though there are some plans for an Xbox 360 emulator at Microsoft. Microsoft had stated they wanted to port some marketplace items and games over to the Xbox One, but they've been quiet since then on the matter.
It would make sense for Microsoft to look back to the original Xbox too; Armed and Dangerous anyone?