theocracy

from The American Heritage® Dictionary of the English Language, 5th Edition.

• noun Government ruled by or subject to religious authority.
• noun A country or state governed in this way.

from The Century Dictionary.

• noun A form of government in which God is recognized as the supreme civil ruler of the state, and his laws are taken as the statute-book of the kingdom.
• noun A state so governed: usually applied, with the definite article, to the Jewish commonwealth from the time of its organization under Moses until the inauguration of the monarchy under Saul.

from the GNU version of the Collaborative International Dictionary of English.

• noun Government of a state by the immediate direction or administration of God; hence, the exercise of political authority by priests as representing the Deity.
• noun The state thus governed, as the Hebrew commonwealth before it became a kingdom.

from Wiktionary, Creative Commons Attribution/Share-Alike License.

• noun Government under the control of a Church or state-sponsored religion.
• noun Rule by God.

from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.

• noun a political unit governed by a deity (or by officials thought to be divinely guided)
• noun the belief in government by divine guidance