The Gollop Chamber allows a psionic soldier to use the Ethereal Device, which unlocks the Temple Ship Assault mission. Candidates must be at Psion rank (1350 Psi XP) and be wearing a Vortex Armor to use the Ethereal Device. The enlisted soldier will be now referenced as the Volunteer and will play a major role on the end game.
The Gollop Chamber may be built after Alien Command and Control research; it cannot be torn down once built.
Activating the Gollop Chamber will head the game to its ending. All research and Foundry projects won't be completed, soldiers won't heal or recover from fatigue and you essentially can't do anything but the Temple Ship Assault mission, so the Chamber shouldn't be activated unless you're prepared for the last mission.
See also