Major Story Arcs
The Chicago Six are the main super-villain group in Chicago, starting after World War II and leading up to the early 1960s. They provide the most significant opposition to the superhero union, C.O.W.L.
The members of the Chicago Six are not all mentioned in the comic. However, John Pierce joins them as a mole, pretending to be a villain but really working for the C.I.A. Eventually he leaves them and joins C.O.W.L. Apparently he had a secret identity as a villain, because when he works for C.O.W.L.--without a mask--only a few select people, including his wife, detective Evelyn Hewitt, and union boss Geoffrey Warner know about his past.
Another member, the Dart, is the original leader of the Six. He is known for his super-speed, and for having injured Sparrow, which eventually caused a rift between him and Warner, and led to Sparrow leaving the union. The Dart is the brother of Blaze. He is never seen on-panel, and his history is partly implied on panel, and partly explained by The League film (see below).
The main known member of the Six is Skylancer. He is a human who uses advanced technology and weapons, some of which he gets through a backdoor deal with Alderman Lowe. One day Lowe meets with him about the technology, but C.O.W.L. finds out and thinks that Skylancer is trying to kidnap or kill the alderman. The union heroes attack, and after a dangerous battle, Radia finally kills Skylancer. At this time, Skylancer was the last of the Six, the others having apparently been killed, captured, or driven away (or in the case of Pierce, returned from undercover). The end of the Six means that C.O.W.L. has no more significant super-powered enemies. This leads the city to want to alter their contract, which Warner and the union don't want, and drives the whole storyline of the C.O.W.L. comic.
Warner eventually asks mob boss Camden Stone to hire some super-powered thugs to make it look like organized super-villains are again on the rise, to take on the role of the Chicago Six so the union can argue for a better contract. These villains, and Stone, are eventually defeated, and the union gets the contract it wants. However, new villains start to rise up on their own, inspired by the Six and Stone's goons, once again giving C.O.W.L. a legitimate reason to exist, and continuing the legacy of the Six.
In Other Media
In the movie The League (which was created before the comic and whose in-universe history is largely although not entirely the same as the comic) various supervillains are named or appear. While they don't use the name "Chicago Six," presumably some of them would have been in the Six if it had been so named, and possibly would have appeared in the comic if the comic series had lasted longer. They include the Dart, whose backstory is explained in more depth, Red Renegade, Big Ivan (who helped created the "Fearsome Five," clearly a forerunner to the Chicago Six), Dmitri Popov, and Nicolai Lennin. All of these except the Dart have Russian names, and one of them may be the template for the Russian Skylancer.