Can You Play Portal 2 Co-op Locally on Xbox? No, Online Only

No, Portal 2 does not support local split-screen co-op on Xbox 360 or Xbox One. The cooperative campaign requires two separate consoles, two copies of the game (or game sharing), and an Xbox Live Gold / Game Pass Core subscription for online play.

This differs from the PlayStation 3 version (which supported split-screen) and the PC version (which supports split-screen via mods or Steam Remote Play Together, but not natively in the same way). On Xbox, the co-op experience is strictly online.

If you want local co-op puzzle-platforming on Xbox, consider titles like Unravel Two, It Takes Two, or Trine 4.