The Overseers’ cancerous anomalous influence on the world is a wound on the fabric of the universe.
A wound that festers cannot heal until the irritant is removed.
The Thirteen Foundation Overseers are the irritant in the wound on our reality.
The Thirteen Foundation Overseers must be removed.
By order of The Engineer, and of Those Who Stepped Down, we stand in defiance of this aberration.
We stand in opposition to this blasphemy against nature.
We stand insurgent against this chaos.
Our path is clear, our vision unclouded. We must clean out the wound. We must let our universe heal.
We must destroy the Thirteen Foundation Overseers.

The Chaos Insurgency first started out in 1924 as a special task force formed by the O5 Council named the "Insurgency". This new task force was comprised of members of the Mobile Task Force Alpha-1, also known as the "Red Right Hand", a special MTF closely associated with the Council, and their leadership was supported by research, security, and retrieval personnel, all taken from Foundation ranks. This task force was secretly created to complete missions with ethically questionable methods and politically unsavory results, while making themselves appear as they were a defecting splinter group from the Foundation, in order to keep the nature and reputation of the SCP Foundation clean.

However, in 1948, after the Insurgency had done another staged raid on one of the Foundation's site, seizing several SCP objects and convincing personnel to join them, the task force went on to do unplanned raids and this time delivering more serious damage to sites and personnel. The Insurgency had decided to betray the Foundation for real due to reasons unknown and renamed themselves the "Chaos Insurgency", much to the shock of the O5 Council. It is later suggested that at some point, the Insurgency came across a powerful anomaly only known as the Engine which could predict futenma and give them steps to follow as part of a bigger plan. The Insurgency's leader who could directly communicate with the Engine became known as the Engineer and went on to attack the Foundation in order to appease the Engine.

Insurrection

Around 1914, as O5-11, Elizabeth Tate, became convinced that the Foundation was mistreating the humanoid

 anomalies under their containment and decided to take matters into her hands after being continually rebuked for her opinions. She and her husband O5-12/The Trainman/The Conductor were able to convince O5-7/The Professor/The Heretic and O5-4/The Gangster into joining them and soon after hiding themselves began to strike various Foundation transports, stealing various artifacts and rescuing some humanoids. Eventually they formed the Chaos Insurgency and planned even more attacks in order for the Council to understand their mistakes.

Ranks:

Delta Command

A group which orders and oversees the activities of the lower ranks. The Engineer is an important member of the Command as they are in constant telepathic communication with the Engine, a paranormal object that controls almost the entire of the Insurgency, although this is up to headcanon. The Engineer constantly transcribes a massive list of instructions comprised of "Plan" and "Steps" which are delivered to the Insurgents by Delta Command. The Engineer and Delta Command appear to be the counterparts of the Foundation's O5 Council and Administrator.

Gamma-class

Chaos Insurgency researchers and military commanders who oversee the execution of orders given by the Command.

Beta-class

Personnel who are under the Gamma-class and carry out orders in the field.

Alpha-class

Are personnel who are often recruited from people who nearly possess no knowledge of the anomalous world. Most of these personnel joined the Insurgency in order to escape from their miserable lives(Or forcefully conscripted) and are considered by the higher ranks as expendable similar to the Foundation's Class-D personnel. They represent the ground forces

Military and R&D divisions

Two divisions that comprise the Insurgency. These two divisions mostly work independently and are unaware of the work of the other cells. Some of these cells include: Consortium Independent; Foundation Feast; Gun Club; Headhunters; Isfet; Nigurath; and Sototh.

This is only a branch out of the Insurgency that has beliefs aligning or disagreeing with other branches. What stands out the most is our Fanatic Orthodox beliefs. May the heretic's woes be many...and their days few.