The objectives are to investigate the feasibility and potential activity of chronic administration of thalidomide in patients with unresectable hepatocellular cancer who receive chemoembolization to predominant tumor masses. The toxicity of thalidomide in these patients will be evaluated. Overall safety will also be assessed. Serum levels of angiogenic cytokines such as VEGF, bFGF, and TNF-a, that are believed to have a role in hepatocellular carcinoma, will be collected.