Bruce Siegel was a longtime denier of all things paranormal or spiritual, and a passionate one. Then something extraordinary happened. He noticed that many of his nightly dreams were coming true. The predicted events were odd, even bizarre, and happened quickly-often just minutes after awakening.

Reluctant to believe what he was seeing, Siegel conducted an experiment that would ultimately span years and involve hundreds of dreams. The result: fully one in four have proven to be precognitive, anticipating future events with striking precision.

A skeptic no longer,...