The problem with defining the alignment of 'society' is that it is very contingent upon whether one defines 'society' as defined by high political movements or broad social movements. I've only got time at the moment to deal with the politics- perhaps I'll put my opinions on society later.
From a high political point-of-view, the usual maxim is that democracies tend to be more chaotic than dictatorships. It is now necessary to revise this view. Lawfulness is based on the inherent regard for tradition, pre-existing laws and rules (especially constitutions in this respect). They are 'conservative' in the true sense of the word, in that they attempt to preserve the status quo. Chaos, by contrast, holds no such regard, rather emphasising the betterment of society (CG), the advancement of self (CE) or a balance thereof (CN), and ignoring any pre-existing laws.
Now let us apply that to democracies and dictatorships. The Roman Emperor, according to Dr Chris Kelly (leading expert on late Imperial Rome), could "abrogate existing laws at will" i.e. one person could conceivably overturn all which had gone before, without constitutional checks and balances. Which does this map more closely? Chaos. Conversely, American democracy, with written constitutions, a sharing of powers (legislative, executive, judicature), a complex electoral college system and a comparative difficulty of constitutional reform (2/3 majority IIRC) is lawful, despite being democratic. Incidentally, of course, it is impossible to map Lawful/Chaotic onto Left/Right- Thatcher and Reagan were far more chaotic than the old Labour leaders of the 70s like Callaghan.
It is important to note that under this high political definition, traditional tribal society is very *lawful*. They continue to worship the traditional gods, continue to follow the same patterns of behaviour, have traditonal customs, traditional dress...it is traditional and continuity which is the sine qua non, not a fluid moulding of the status quo. Elected chieftains does not alter this. It is further important to note that 'chaotic' behaviour does not indicate a lawful society: the Vikings are cited as chaotic in pillaging etc., but their basic society is one rooted in the past, hence their strong grounding in sagas and mythology.
Simply put, therefore, IMO, the single determining factor of lawfulness/chaos in terms of politics is one's attitude towards the status quo. Lawfuls tend to see an inherent regard in it (see Burke) as a culmination of factors. They regard its existence as self-evident of its empirical value (Hegel: "What is actual is rational"). Chaotics repudiate it, seeking to build a new society from the ground up...placing minimal value in it and regarding it as no better than any other theorised or postulated model. Neutrals fall somewhere in between.
In conclusion, therefore, it is possibly to have a chaotic society, but it would be rare. A society constantly in state of flux would be chaotic, but rarely would it be successful. Nineteenth-century France, with its myriad of different and contradictory regimes (First Republic, Directory, Napoleonic Empire, Restored Bourbon Monarchy, Orleanist Monarchy, Republic, Second Empire, Third Republic, Commune...) would probably be the best example of a chaotic society, with successive models being instituted and the status quo being routinely cast aside. Revolutions, not mere radical reform (which is neutral with chaotic tendencies) would be commonplace. Regimes would come and go. Laws would be made and broken. A chaotic society can exist, but I, for one, would not wish to live there.