The word anarchy typically conjures up images of chaos, disorder, and violence, yet Christian anarchy is quite different from this. Vernard Eller defines the position as the state of being unimpressed with, disinterested in, skeptical of, nonchalant toward, an uninfluenced by the grandiose claims of any and all principles of governance claiming to be of primal value for society. While the Christian Right and the Christian Left have both fallen prey to the seduction of the wealth and power of the state as a means to promote their social values and respective political agendas, Christian anarchists claim exclusive allegiance to the kingdom of God and thus refuse to utilize systems of power, whether the state or any other form of political hierarchy, to impose their views on others.
Christian anarchy is distinctively non-violent and is disinterested in political revolution, as revolutionaries seek to subvert one system of power only to replace it with another. It is disinterested in political activism on the same grounds, viz. that the state is ultimately rooted in power and violence. Christian anarchists obey the laws of the state so long as they do not conflict with the law of God (cf. Rom 13; Ac 4:19-20), but largely ignore the government and its mythological pretention to primacy as they go about the business of advancing the kingdom of God.
This is not, however, to suggest that Christian anarchists are quietist or isolationist; they are quite the opposite, actively engaged in doing good through voluntary free associations of individuals (a.k.a. churches or congregations). But the good that they do is not done in the name of humanity, philanthropy, or a more perfect state; it is done solely in the name of Christ and for His glory.
Soli Deo gloria!