Joining a Chaos district will put you into a survival mode that allows you to gain points by killing as many players of the opposite faction as possible. All of the district's contacts are gone, replaced by vendors. So there's no other mission but to kill, and kill quickly. A leaderboard tracks the best of the best and several new titles and a new role have been added.
You can check out an early prototype of Chaos Mode in the game between now and June 6.
[Thanks to Derek for the tip!]