It's 2:30 in the afternoon in the Dominican Republic, and Karen Velline, a 66-year-old grandmother from Cold Spring, Minnesota, is lying on an operating table, swaddled in sterile surgical sheets. She's just moments away from a procedure so experimental that no doctor will perform it on U.S. soil. Yet she calmly stares up at the ceiling, more excited than anxious. Despite the controversy surrounding it, Velline believes that this procedure—which she has paid Regenocyte Therapeutic, a stem-cell company in Bonita Springs, Florida, $64,000 in cash to perform—could save her from a debilitating lung condition. After months of anticipation and planning, she's ready for things to get under way.