The Redacted Chamber is unlocked by finding it's module in the Museum level in story mode.
It's located right next to the Reclamation bin which is about halfway through the level next to the Monomat vendor.
As soon as the module is put into the bin it will appear on the switchboard in the Menu area and the Redacted Chamber will be available to play.
To access it, use the large screen in the middle of the Menu area and switch from Story Mode to Sandbox then select Redacted Chamber from the menu below.