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In 2006, the same year Venezuelan President Hugo Chávez called then U.S. President George W. Bush “the devil” at the U.N., Chávez and his oil-rich, anti-U.S. revolution were looking for new ways to kick Washington in the shins. But there was one move that year that made even some diehard Chavistas uncomfortable: strengthening Venezuela’s alliance with oil-rich, anti-U.S. Iran and its erratic new President Mahmoud Ahmadinejad. Iran wasn’t just another strident U.S. foe; in the eyes of much of the world it was a tyrannical, terrorist-friendly pariah. Hardline leftists like his then chief of staff, Delsy Rodríguez, egged Chávez on, but others in his government saw more drawbacks than benefits to the Caracas-Tehran abrazo.

Their concerns of course were...