In previous research, the drug lamivudine was shown to stop the growth of the hepatitis B virus and to lead marked decreases in the levels of hepatitis B virus and to improvements in the disease in 50 to 70% of patients. However, once lamivudine therapy was discontinued the virus returned to levels noted before the therapy began. In those studies lamivudine was given for 3 to 12 months then discontinued. This study will investigate the safety and effectiveness of long-term therapy with lamivudine.