It looks like the "extremely rare" Xbox One will be available only through a sweepstakes in Microsoft's Bing Rewards program. To enter, you'll have to create an account if you don't already have one, and spend points you earn by using Microsoft's search engine to enter a chance to win.
The custom Xbox One comes with a copy of Battlefield Hardline, a 12-month EA Access subscription, and without a Kinect.
This sweepstakes ends on February 26 at 9:00 AM ET and winners will be announced on March 17. You can find out more about the sweepstakes and its official rules here.