Sorafenib Tosylate Before and After Hepatic Arterial Chemoembolization With Doxorubicin Hydrochloride and Mitomycin C in Treating Patients With Localized Liver Cancer That Cannot Be Removed by Surgery

Inclusion Criteria * Age \> 18 years old * Confirmed HCC diagnosis by Biopsy or Radiologic parameters. Following NCCN guidelines for HACE, including subjects within the University of San Francisco transplant listing criteria. * ECOG Performance Status 0 or 1 * Adequate bone marrow, liver and renal function as .assessed by the following: * Hemoglobin \> 9.0 g/dl * Absolute neutrophil count (ANC) \> 1,500/mm3 * Platelet count \> 75,000/mm3 * Total bilirubin \< 2 mg/dl * ALT and AST \< 2.5 times the ULN ( \< 5 x ULN for patients with liver involvement) * Creatinine \< 1.5 times mg/dl * Women of childbearing potential must have a negative serum pregnancy test performed within 7 days prior to the start of treatment * Women of childbearing potential and men must agree to use adequate contraception (barrier method of birth control) prior to study entry and for the duration of study participation. Men should use adequate birth control for at least three months after the last administration of sorafenib. * Ability to understand and the willingness to sign a written informed consent. A signed informed consent must be obtained prior to any study specific procedures. * INR \< 1.5 or a PT/PTT within normal limits. Patients receiving anti-coagulation treatment with an agent such as warfarin or heparin may be allowed to participate. For patients on warfarin, the INR should be measured prior to initiation of sorafenib and monitored at least weekly, or as defined by the local standard of care, until INR is stable. * BCLC Stage B (Intermediate) * multinodular asymptomatic tumors * without vascular invasion * without extrahepatic spread * Child Pugh A through B7 * Male or female patients \> 18 years of age * Life expectancy of at least 12 weeks. Patients with unresectable, multinodular asymptomatic tumor (no vascular invasion or extrahepatic spread) * Patients with histologically or cytologically documented HCC. Documentation of original biopsy for diagnosis is acceptable if tumor tissue is unavailable * Prior informed consent. * At least one tumor lesion that meets both of the following criteria: * The lesion can be accurately measured in at least one dimension according to RECIST * The lesion has not been previously treated with local therapy (such as surgery, radiation therapy, RFA, PEI, or cryoablation) Exclusion Criteria * Cardiac disease: Congestive heart failure \> class II NYHA. Patients must not have unstable angina (anginal symptoms at rest) or new onset angina (began within the last 3 months) or myocardial infarction within the past 6 months. * Known brain metastasis or CNS disease. Patients with neurological symptoms must undergo a CT scan/MRI of the brain to exclude brain metastasis. * Cardiac ventricular arrhythmias requiring anti-arrhythmic therapy. * Uncontrolled hypertension defined as systolic blood pressure \> 150 mmHg or diastolic pressure \> 90 mmHg, despite optimal medical management. * Known human immunodeficiency virus (HIV) infection * Active clinically serious infection \> CTCAE Grade 2 except hepatitis B or C. * Thrombolic or embolic events such as a cerebrovascular accident including transient ischemic attacks within the past 6 months. * Pulmonary hemorrhage/bleeding event \> CTCAE Grade 2 within 4 weeks of first dose of study drug. * Any other hemorrhage/bleeding event \> CTCAE Grade 3 within 4 weeks of first dose of study drug. * Serious non-healing wound, ulcer, or bone fracture. * Evidence or history of bleeding diathesis or coagulopathy * Major surgery, open biopsy or significant traumatic injury within 4 weeks of first study drug. * Use of St. John's Wort or rifampin (rifampicin). * Known or suspected allergy to sorafenib or any agent given in the course of this trial. * Any condition that impairs patient's ability to swallow whole pills. * Any malabsorption problem. * Use of any prior systemic chemotherapy or targeted agents. * Diffuse HCC or presence of vascular invasion (including segmental portal obstruction), extrahepatic spread * Advanced liver disease: unstable ascites or \>Child-Pugh B7 * Porto-systemic shunt * Any contraindication for an arterial procedure such as impaired clotting tests (platelet count \< 50.000/mm3 or prothrombin activity \< 50 percent), 1 * Renal failure * Severe atheromatosis * Any contraindication for systemic chemotherapy administration (serum bilirubin \> 5mg/dL, leukocyte count \< 3.000 cells/mm3) * Any contraindication for sorafenib administration * Patients with clinically significant gastrointestinal bleeding within 30 days prior to study entry * Substance abuse, medical, psychological or social conditions that may interfere with the patient's participation in the study or evaluation of the study results * Pregnant or breast-feeding patients * Previous or concurrent cancer that is distinct in primary site or histology from HCC, EXCEPT cervical carcinoma in situ, treated basal cell carcinoma, superficial bladder tumors (Ta, Tis \& T1). Any cancer curatively treated \> 3 years prior to entry is permitted * Patients receiving therapy for Hepatitis A, B or C * Encephalopathy ≥ Grade 1.