The Xbox One was designed with a different infrastructure than the previous consoles in the Xbox line, making direct backwards compatibility impossible. Instead, the operating system of a previous console would have to be emulated, so that older games could run.
A few weeks ago, Microsoft made this a reality by offering backwards compatibility using an emulated version of the Xbox 360 as part of its New Xbox One Experience. There have been hints that emulation of the original Xbox console is also possible, though fans shouldn't start holding their breath just yet.
According to Xbox engineering boss Mike Ybarra, when it comes to bringing Xbox games to the Xbox one "nothing's impossible." He added that the team wasn't working on original Xbox emulation yet, however; the team's current focus is "making more Xbox 360 games work." Going back to emulate the original Xbox would be a challenge to the team, and it's one they're not likely to undertake while still actively working to expand the Xbox 360 titles the Xbox One can play.
This isn't the first time that the subject has been mentioned, of course. Xbox boss Phil Spencer also suggested the possibility back in August, stating that he asks the backwards compatibility team about original Xbox compatibility a lot. However, he added that the team "[needs] to finish 360 backwards compatibility for now."
Using emulation to accomplish backwards compatibility opens a lot of opportunities for classic favorites, but it's unlikely that we'll see original Xbox games on the Xbox One anytime soon. Ybarra stated the team was looking to add new 360 games at a "high frequency," so it's clear the more recent console is the backwards compatibility team's main focus. Given that it took a few years for the team to develop Xbox 360 emulation, even if they were working on Xbox emulation, it might not be ready for release until much later.
Still, Ybarra admits the team loved a challenge and he was "sure they would love [the original Xbox] as an opportunity to go look at." Adding Xbox compatibility could also add value to the console's golden years, providing some additional revenue and possibly even a slight sales boost, as the focus shifted to its eventual successor. The only question is whether Microsoft would consider it worth its time to develop emulation for older games that late in the console's lifespan.