This is a clinical trial to test the safety and efficacy of the drug thalidomide in combination with a procedure called chemoembolization in patients with inoperable liver cancer. Chemoembolization is the process by which chemotherapy is instilled directly into the blood vessels feeding the tumor, so that the blood vessels feeding the tumor may be blocked. Chemoembolization consists of two separate procedures. It will be done by infusing chemotherapy with the drug doxorubicin through the hepatic artery into the liver and then by infusing collagen to cut off the blood supply to the tumor. A catheter will be inserted at various times to allow for these infusions.