Update: Tipster H20 Acidic has confirmed Left 4 Dead 2 does run on the Xbox One. Here are some instructions he submitted to Shacknews on how to get Left 4 Dead 2 running on the Xbox One:

Step 1: On your Xbox One, search for the gamertag: h2o acidic (That’s an o and not a Zero)
Step 2: Go into that profile and look at following/followers click by game if needed.
Step 3: Find Left 4 Dead 2 and select and then click go to store. From there you’ll see a box “loading”, which normally it’ll be the area it says bundle only. After it loads you’ll see INSTALL.
Step 4: Download/Install.

Here's also a video showing Left 4 Dead 2 on his Xbox One:

Original Story:

The Witcher 2 was just added to the Xbox One backwards compatibility list, and as a reminder, is currently free until February 5. But we’re hearing rumors Valve’s classic 4-player co-op shooter, Left 4 Dead 2, may soon be added to the backwards compatibilty list.

According to a Reddit user, their source was able to install Left 4 Dead 2 on their Xbox One by going to the Xbox website and initiating a download. According to the user, their source was able to run the game and showed it running on their console, although the image doesn’t really show anything that indicates it’s running on an Xbox One.

We’ve seen leaks of future Xbox One backwards compatible titles in the past, including Fable III, so it’s completely possible a user was able to download Left 4 Dead 2 onto their Xbox One due to its upcoming backwards compatible release. Considering we’ve seen no definite proof aside from various screenshots of the game’s details on the Xbox Store, we’ll chalk this up as a rumor until we get more concrete evidence.