The Staff of Chaos (also known as the Balac-thurm) is a highly powerful, magical artifact that was fashioned in the early First Era by Loreth. The staff was deemed too powerful and was hidden in the catacombs beneath the city of Mournhold. Jagar Tharn (Imperial Battlemage to Emperor Uriel Septim VII) managed to obtain it by manipulating the Dunmer queen Barenziah, either by disguising himself as a bard known as "Nightingale"  or by employing Drayven Indoril to fill the role. 
Tharn used the staff to transport Uriel Septim VII and his personal guard to a plane of Oblivion, then used a spell to make him look like Uriel Septim, next broke the Staff of Chaos into eight pieces and hid the pieces all around Tamriel. The Eternal Champion had to go and collect all eight pieces and use the staff on Tharn to defeat him and bring back the Emperor and his personal guard and end the Imperial Simulacrum.
After the Eternal Champion touched the Jewel of Fire with the Staff of Chaos the magical items disappeared, while at the same time Uriel Septim and his guard were brought back to Mundus. Most people believe the Staff was either somehow destroyed or banished into Oblivion, though both ideas were considered impossible before the Simulacrum.
Pieces of the Staff
The eight pieces are in:
- Fang Lair in Hammerfell
- Labyrinthian in Skyrim
- Elden Grove in Valenwood
- Halls of Colossus in Elsweyr
- Crystal Tower in Summerset Isles
- Crypt of Hearts in High Rock
- Murkwood in Black Marsh
- Dagoth-Ur in Morrowind
- The Elder Scrolls: Arena
- The Elder Scrolls II: Daggerfall (mentioned only)
- The Elder Scrolls V: Skyrim (mentioned only)
- The Elder Scrolls Online (mentioned only)
- In The Elder Scrolls Online, Sheogorath mentions rebuilding the Staff of Chaos to the Vestige, around 750 years prior to it's assemblege by the Eternal Champion in 3E 399.