Not necessarily, timothy. That you obey rules doesn't mean that they are the same rules that everyone else obeys.
Think of the baatezu. Pit Fiends, for example. They are the personification of Lawful Evil, beings born of the very law. You can't get much more lawful than that.
Now, summon a pit fiend in a somewhat nice and ordered society like Athkatla, and see what it does to the presumably also lawful city guards.
Lawful doesn't mean that you obey the laws, it means that you obey some sort of inner moral code. If that moral code says that you must kill all who have brown hair, it's not a problem. To the alignment, at least.
Likewise, being chaotic doesn't mean that you don't obey the laws, it means that you are unpredictable, change your opinions often and think that "I feel like it" is a good enough reason for anything up to and including genocide.
At least that's how I understood the DnD alignment system. I could be mistaken.
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