Could the Xbox One emulate the 360?

There will not be any backward compatibility for the Xbox 360 on the Xbox One. Unusual position for Microsoft as typically they are all about the compatibility with older versions of their products. However in this case it makes sense as the hardware is significantly different between the two systems.

But I do have a thought about this. Given that the Xbox One is running three operating systems could the hypervisor in the new console run an emulated version of the Xbox 360 operating system?

It would not be a simple task to accomplish this but I believe it is within the realm of possibility. Even back in 2011 people were talking about creating an Xbox 360 emulator on a PC, and there is apparently now a working Xbox 360 emulator available for both PC and Mac.