Microsoft revealed backwards compatibility for the Xbox One at this year's E3, though this only extends to Xbox 360 games and not games from the original Xbox era. This could however change in the future, as Xbox chief Phil Spencer answered a fan question about the matter on Twitter and said:
"I don't think it's silly. I ask the BC team this question a lot. Need to finish 360 BC for now."
While this is far from a confirmation of a compatibility extension, Spencer is at least interested in the idea, and might look further into it, once they are satisfied with Xbox 360 backwards compatibility.