This thread has spun around so many times I'm dizzy. Real world examples, fantasy/book/movie examples, blah, blah, blah. We can't define any of the terms we use. Where to go? How about this for a new shot at it.
Lawfulness cannot in itself be defined in terms. Chaos cannot be defined in terms either. But if we look at them as order and disorder (almost like the thermodynamics definition of chaos), we can put them to some use. Law and chaos can only be truly defined in terms of each other, but sometimes a circular argument is what you have to deal with...
The supremely lawful society or culture (I prefer culture as the reference point) has made every effort to banish disorder through whatever means (laws, traditions, programs); everybody knows the 'rules' and how they fit into the picture. You could illustrate this entire culture with a standard outline structure and org-chart. A supremely lawful individual has made every effort to banish disorder from his or her personal life, affiliations and desires.
The supremely chaotic society or culture has made every effort to banish order, through whatever means. This culture has no structure whatsoever. Even concepts such as power are meaningless, since that would inflict a type of order all its own. The desires of the supremely chaotic individual are paramount, with no concern for good or evil, or frankly anything other than that individual's perceptions at a particular moment.
Neither vision can be fully realized, but we can see where different cultures or individuals fall within the spectrum. As there is no number that is mathematical infinity, there can be no example of the 'perfect' Law or Chaos. The only reason that the lawful situation is a bit easier to describe is that thought itself is the collection and organization of ideas, concepts and their relationship to each other. A pure chaos would be characterized by madness, a pure lawfulness would be characterized by rigid adherance to the structure, even if logic dictated otherwise. Logic or reason (in some form or other) mitigates both structure and madness into the variety of behaviors that cultures and individuals display. A pure lawfulness or chaos could drift to goodness or evil freely, or ignore both (passively neutral), or consider both (actively neutral).
This is only in regards to the D&D alignment system. It probably holds no water in any real world situation (kind of like the simplistic concept we call Armor Class).
-Fletch!