Update - Citing a "technical glitch," Square Enix told Shacknews that the Xbox 360 demo has been taken offline. It promises that it will announce the official availability across both Xbox 360 and PlayStation 3 sometime later, but for the time being, it's gone. Unless you grabbed it quickly, you'll just have to wait for Lightning to strike twice.
Original Story - A demo for Lightning Returns: Final Fantasy XIII has hit Xbox Live, in preparation for the game's February launch. It's a Gold exclusive, though, and hasn't gone up on the PlayStation Network quite yet.
The demo (via Polygon) weighs in at 1.14 GB. You can try out the battle system and costume customization features, as well as the "Outerworld" services that let you share screenshots and scores. If you activate Outerworld in the demo, you'll be rewarded with Siegfried garb once the full game comes out on February 11.
Shacknews has contacted Square Enix regarding a PS3 demo.