Black Zero is a name shared by two supervillain, two terrorist organizations, one special forces group, and a computer virus that have all appeared in various comic book series published by DC Comics.
The original Black Zero appeared pre-Crisis in Superman (vol. 1) #205 (1968), in a story entitled "The Man Who Destroyed Krypton" written by Otto Binder with artwork by Al Plastino. This Black Zero revealed to Superman that he was a space saboteur who destroyed planets. He had been hired to destroy Krypton, and discovered that the internal stresses which would have destroyed it in any case were dying down, necessitating his involvement to ensure it exploded.
In the present day, Black Zero came to Earth, threatening to destroy it as he did Krypton. In desperation, Superman released Jax-Ur, a prisoner of the Phantom Zone, who wished to avenge Krypton's destruction. As he launched a devastatingly powerful missle toward Earth, Black Zero attacked Jax-Ur with a red Kryptonite bullet, causing his body to mutate wildly into several serpent-like forms. This proved to be Black Zero's undoing; While Superman saved the Earth from the missile, Jax-Ur transformed into a Medusa-like form, turning Black Zero to stone with his gaze. Black Zero's body was then shattered by Jax-Ur, in recompense for what he had done to Krypton.
This story suggests that were it not for something none of them knew, Jor-El would have been wrong and the Science Council right. E. Nelson Bridwell hypothesized that what Black Zero had noticed was the Green Lantern Tomar Re's attempts to prevent the destruction (as seen in Superman (vol. 1) #257 (1972)), meaning the two sets of interference canceled each other out, and Jor-El was right.
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Links: Wikipedia Entry Black Zero Profile DC Universe Guide