Pompe disease is an inherited condition of acid alpha-glucosidase (GAA) deficiency resulting in lysosomal accumulation of glycogen in all tissues. Glycogen accumulation leads to muscle dysfunction and profound muscle weakness. A wide spectrum of disease is characteristic and the most severe patients have cardiorespiratory failure, often fatal in the first two years of life. Researchers have developed a way to introduce the normal GAA gene into muscle cells with the expectation that the GAA protein will be produced at levels sufficient to reduce glycogen accumulation. This study will evaluate the safety of the experimental gene transfer procedure in individuals with GAA deficiency. The study will also determine what dose may be required to achieve improvement in measures of respiratory function.