A few centuries before the events of the Divergent Trilogy, The United States Government became interested in enforcing certain desirable behaviors in its citizens. There had been studies that indicated that violent tendencies could be partially traced to a person's genes, to a gene named the murder gene. They soon found more genetic predispositions toward cowardice, dishonesty, low-intelligence, selfishness and cruelty -all qualities that contribute to a broken society. The government tried to reduce the risk of these undesirable qualities showing up in the population by correcting them, in other words, by editing humanity.
A genetic manipulation experiment was born. People were selected in large numbers, according to their backgrounds and behaviour, and they were given an opportunity to give a gift to the future generations, a genetic alteration that would make their descendants just a little bit better. But when the genetic manipulation began to take effect, the alterations had disastrous consequences. As it turns out, the attempt had 'corrected' some genes, but damaged others.
For example, when they took away someone's fear, you take away their compassion. Take away someone's aggression and you take away their motivation, or their ability to assert themselves. Take away their selfishness and you take away their sense of self-preservation.
Humanity was never perfect, but the genetic alterations had made it worse than ever before. That manifested itself in what was called the 'Purity War'. When the war was over, the people demanded a permanent solution to the genetic problem.
The Bureau of Genetic Welfare was created to try to counter the genetic problem. They designed experiments to restore humanity to its genetically pure state. They called for genetically damaged individuals to step forward so that the Bureau could alter their genes. The Bureau the placed them in secure environments to settle in for the long haul, equipped with basic versions of the serums to help them control their society. The Bureau would then wait for each experiment to produce genetically healed humans, or as they known inside the experiements, Divergents.
If you are Divergent, your genes are pure, whole and restored.
Chicago, was one of many experiments, and the most successful one. There are only 3 active experiments at the time of the trilogy.