OUTLINE: Patients receive oral sorafenib tosylate twice daily on days 1-14. Beginning ≥ 3 days later, patients undergo hepatic arterial chemoembolization (HACE)* with doxorubicin hydrochloride and mitomycin C. Beginning ≥ 3 days after the completion of HACE and/or once liver function returns to baseline, patients resume sorafenib tosylate twice daily for up to 6 months in the absence of disease progression or unacceptable toxicity.