The Shadow Chamber facility is basically an upgraded version of the Laboratory. It gives access to new research projects, which are otherwise unavailable. Additionally, there's no point to construct this facility early in the game, as research projects here take monstrous amounts of time to complete, will pause "normal" research projects, and all of the things that you research here are story-related, meaning that you simply won't have anything to do here when you rush this facility.
The recommended time to construct this facility is when you have at least 5 scientists.
Upgrades and staff influence
Construction takes 20 days.
Monthly upkeep cost - 30x Supplies.
- Allows you to perform more advanced research projects, which are required to push the story forward.
Psionic Gate: gives access to further research projects.
Cost: 200x Supplies, 4 Power. Monthly upkeep cost - 50x Supplies.
Additionally, the Shadow Chamber allows you to see what types of enemies, as well as their overall number you will have to face on a mission. It can be checked on the mission screen, in the upper right corner of it, right before you enter the briefing stage, where you can select the equipment for your soldiers.