Anarchy doesn't have to mean chaos. The government and individuals could easily defend themselves from anonymous attacks if they utilized proper information security.
There is a distinction between the commonly held meaning of anarchy (as chaos) and the political philosophy (which is why there are 2 asterisks).
Anarchism the political ideology believe that order doesn't not have to come from a centralized state via force. Rather it can happen organically... since the vast majority of humans desire order. We all value security, eatting, etc.
The difference is that order is maintained not via coercion by a central authority but by individuals, communities or markets (depending on the various branches of anarchy).
This book explores the concept very well and is heavily cited in philosophy circles:
anarchy |ˈanərkē|
noun
* a state of disorder due to absence or nonrecognition of authority: he must ensure public order in a country threatened with anarchy.
* absence of government and absolute freedom of the individual, regarded as a political ideal.
[New Oxford American Dictionary, Dictionary.app, OS X 10.7]
If you want to convince me that this definition is wrong, show me why it's not a valid concept to hold, given the facts of reality.