I think there's a fundamental issue with the idea of a "chaotic society", in that a "society" is a long-term, large scale structuring of people. So, we are asking "what does a chaotic structure" look like, and that's hard.
There's two different forms we can consider - in one, the structure of society is chaotic, and in the other the behaviors of society are chaotic.
When a society is chaotic in structure, that means that whatever definable bits it has (families, clans, towns, guilds, etc) change and re-align rapidly and frequently. If it is a Chaotic Good society, they do this because that gets stuff done quickly and efficiently for everyone's benefit - they agree upon goals, and they each pitch in as is most effective, without having to be told by authority or tradition how it has to happen. In a Chaotic Evil society, this happens because everyone's trying to claw to the top the best they can, taking each and every opportunity as it comes up.
When a society's behavior is chaotic, the response of that society to events cannot be predicted. It can have a very structured process for making decisions, but for whatever reason, those decisions vary wildly from one moment to the next.