China, with lower regulatory hurdles, is racing to a lead in gene therapy. Once a week, Hashmukh Patel, a 62-year-old retired semiconductor engineer from Silicon Valley, travels with his wife, Bena, from their Beijing hotel to Beijing-Haidian Hospital. They ride the crowded elevator to the ninth floor, enter a pleasant, sun-filled ward with private rooms, and Patel gets an injection that he hopes will save his life. Suffering from late-stage cancer of the esophagus, he has come to Beijing for a Chinese gene-therapy drug called Gendicine that's supposed to kill tumor cells. Patel tried just about everything before coming to...