In a very strange issue that is only effecting Xbox One players, Epic Games have taken to Twitter to address an issue that Fortnite players on the Xbox One are experiencing stability issues.
Epic Games have noted that while they are looking into the issue, they have found a quick fix which involves you disconnecting your Kinect. The company states:
We’ve identified that Xbox One players with a Kinect plugged in may encounter stability issues when starting up Fortnite. We’re investigating a fix for this issue, but players can work around it in the meantime by disconnecting their Kinect.