An example of a purely chaotic society would be the wildlings from A Song of Ice and Fire by George RR Martin. Contrasting strongly to the orderly folk of Westeros whose family ties and orders of knights form the basis of society. The wildlings reject this, they have no laws, no king, not even marriage. There's a guy they follow around and respect, but he can't really tell them what to do.
I filed the serial numbers off this for my campaigns' barbarian tribes. It was rather frustrating when the PCs tried to deal with them.
PC: Who is your leader?
Barbs: We have no leader. Each warrior does as he pleases.
PC: Okay...well is there a representative, someone who can speak for the tribe?
Barbs: No barbarian may presume to speak for another.
PC: Well, how can I get the tribe to listen?
Barbs. I dunno. Talking?
I filed the serial numbers off this for my campaigns' barbarian tribes. It was rather frustrating when the PCs tried to deal with them.
PC: Who is your leader?
Barbs: We have no leader. Each warrior does as he pleases.
PC: Okay...well is there a representative, someone who can speak for the tribe?
Barbs: No barbarian may presume to speak for another.
PC: Well, how can I get the tribe to listen?
Barbs. I dunno. Talking?