You need to figure out what "chaotic" means to even begin to figure out what a chaotic society is. Personally, I don't think there is a meaning that can be meaningfully and consistently applied to D&D societies without radically redefining the way that D&D societies are typically thought of (cities=lawful, primitive tribes and elves=chaotic, etc). The reason for this is that, IMO, the D&D concept of Chaos artificially links a number of ideas that have no actual real world correlation.
For instance, one possible (and very common) interpretation of chaotic is "placing personal, individual freedom as their pre-eminent value." This is contrasted with traditional societies which view group attachments, family honor, etc as pre-eminent. So, by that standard, the Protestant reformation was, by and large, a chaotic movement and the United States is one of the most chaotic societies on the planet.
On the other hand, chaotic is just as often defined as a preference for evaluating individual cases individually as opposed to evaluating them by set laws and standards. Thus the followers of an autocrat who is not bound by his own laws or who had the power to decide the when laws applied and what exceptions could be made would constitute a chaotic society. By this standard, the United States, at times, Ancient Rome and other societies which notably uphold the idea of the rule of law--epitomized in the phrase, "a nation ruled by laws rather than by men" are profoundly lawful. Similarly, by this standard, the Protestant Reformation which hearkened to a strict literal interpretation of scripture as opposed to the authoritative interpretation of scripture through a living church tradition would be a lawful movement rather than a chaotic. And traditional societies--such as many middle eastern monarchies--where the rulers wield more or less absolute and arbitrary power (over peoples who tend to identify as groups more than individuals and value things like family honor) would be considered chaotic rather than lawful.
Then there are more personal interpretations of law and chaos--a lawful person has ordered and considered thoughts and opinions that aren't likely to change/a chaotic person changes from one moment to the next. By this standard chaos comes to mean inconsistency (and, in extreme interpretations, insanity).
Or a lawful person has a tendency to obey existing authority structures/ a chaotic person is a rebel. By this standard, law/chaos is a relative standard as the East German political prisoner who is a chaotic rebel in the East German context becomes lawful when he is freed and becomes a member of the Bundesrat in the reunification. And George Washington is chaotic while leading the armies of the American Revolution but becomes lawful when Cornwallis surrenders.
IMO, the ideas generally linked to the law/chaos axis of D&D alignment don't belong together and, when just one idea is picked, it doesn't come close to the significance of good and evil in most peoples' thought. Which is why I tend to ignore it myself.
