In this study a modified virus called adeno-associated virus (AAV) will be used to transfer a normal gene for human clotting factor IX into patients with severe hemophilia B (AAV human Factor IX vector). Gene therapy is a very new medical technique being used in a number of clinical studies for diseases such as cancer and cystic fibrosis. At this time, the U.S. Food and Drug Administration has approved no gene transfer products for commercial use. To date, 8 subjects have received AAV vector in the muscle for a hemophilia B trial by intramuscular injection, and, to date, 6 subjects have been treated with AAV vector in the current hemophilia B liver trial. Eleven cystic fibrosis subjects have received AAV vector into their nasal sinuses or lungs to date. In this study, AAV human Factor IX vector will be injected into the liver using a catheter inserted into a large blood vessel (called the proper hepatic artery or the right hepatic artery).