AAT deficiency is a genetic disorder in which individuals have inadequate levels of the AAT protein. AAT protects the lungs from white blood cell enzymes that can damage air sacs within the lungs, potentially leading to emphysema. Experimental gene transfer procedures, in which normal copies of genes are inserted into cells, are being developed to treat many genetic diseases, including AAT deficiency. In this study, a modified virus, adeno-associated virus (AAV), has been genetically engineered to contain a normal copy of the AAT gene. When AAV is combined with the AAT gene, the resulting agent, Recombinant Adeno-Associated Virus Alpha 1-Antitrypsin (rAAV1-CB-hAAT) Gene Vector with a chicken beta actin promoter (CB), may be able to carry normal copies of the AAT gene into muscle cells with the expectation that additional AAT would be produced. The purpose of this study is to evaluate the safety of injecting rAAV1-CB-hAAT into individuals with AAT deficiency.