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Iran’s continued unrest, now extending through the 31st anniversary of the revolution that toppled Shah Mohammad Reza Pahlavi, raises the question of whether the Islamic Republic is about to fall. As in 1979, millions of Iranians have taken to the streets, this time to protest electoral fraud in the presidential vote last June.

The cheated presidential candidates, both veterans of the revolution, instinctively thought of a replay of history. Mir Hossein Mousavi saw the green symbols of the demonstrators as representing the color of the House of the Prophet, and urged his supporters to continue their nightly rooftop chants of “God is great!” Thus, the first slogan of the opposition invoked the religious...