The purpose of this study is to determine the response rate and time to progression of the combination of thalidomide, alfa interferon, and octreotide (Sandostatin LAR) in patients with unresectable hepatocellular carcinoma. If patients are eligible for and agree to take part in the study, they will be assigned to one of two treatment arms depending on SSR status. If SSR status is positive or unknown, patients will receive oral doses of thalidomide starting at 200mg a day and increasing to 800mg at increments of 200 per week depending on tolerance. They will also receive injections three times a week of alpha interferon and monthly injections of octreotide (Sandostatin LAR) 30 mg into their buttocks muscle..