Study of Sorafenib and Transarterial Chemoembolization (TACE) to Treat Hepatocellular Carcinoma

Inclusion Criteria: 1. Unresectable hepatocellular carcinoma (HCC) patients with liver-predominant disease as described in section 5.1, or patients with hepatocellular carcinoma who refuse surgery. No more than 30% of the cohort should have macrovascular invasion and/or asymptomatic extrahepatic disease. Multifocal HCC is acceptable, no diffuse HCC. 2. Age \> 18 years old 3. Eastern Cooperative Oncology Group (ECOG) performance status of 0-1 4. Childs class of A or B (up to 7) (see Table 5.0) 5. Adequate end-organ function as manifested by: * Absolute neutrophil count of \> 1500/mm3 and platelets \> 50,000/mm3 * Creatinine ≤ 2.0 * Aspartate aminotransferase (AST), Alanine aminotransferase (ALT) \< 5 x upper limit of normal (ULN) * Total bilirubin of ≤ 3 * Albumin \> 2.0 * International normalized ratio (INR) \< 2.0 * Leukocyte count \>3000 cells/mm3 6. Amylase and lipase ≤ 1.5 the upper limit of normal 7. Patients who have received previous hepatic surgery , radiofrequency ablation (RFA), percutaneous ethanol injection (PEI), or cryoablation are eligible if target lesion(s) have not been treated and local therapy completed \> 6 weeks prior to entry. 8. Left ventricular ejection fraction ≥ 45% 9. Patients with asymptomatic HIV infection are not eligible 10. Willingness of male and female subjects, who are not surgically sterile or post menopausal, to use reliable methods of birth control for the duration of the study and for 30 days after the last dose of study medication. 11. Patient must have signed informed consent prior to registration on study. 12. Resolution of all acute toxic effects of any prior local treatment to Common Terminology Criteria for Adverse Events (CTCEA) Grade 1 or 0. 13. At least one tumor 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) unless it has shown progression in the interim. Exclusion Criteria: 1. Patients unable to swallow oral medications 2. Prior embolization, systemic or radiation therapy for HCC (liver) 3. Tumor burden in the liver exceeding 70%. 4. Complete occlusion of the entire portal venous system 5. Ascites refractory to diuretic therapy (minimal or trace on imaging is acceptable) 6. 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, and T1). Any cancer curatively treated \> 3 years prior is permitted. 7. Patients with clinically significant gastrointestinal bleeding within 30 days prior to study entry 8. History of bleeding within the past 4 weeks (unless deemed by PI as clinically insignificant, for ex., a brief episode of epistaxis) 9. Any contraindication to doxorubicin administration 10. Evidence of severe or uncontrolled systemic diseases, 11. Congestive cardiac failure \> New York Heart Association (NYHA) class 2, myocardial ischemia within 6 months, active coronary artery disease, cardiac arrhythmias requiring anti-arrhythmic therapy other than beta blockers or digoxin, unstable angina, or laboratory finding that in the view of the investigator makes it undesirable for the patient to participate in the trial 12. Any prior history of hypertensive crisis or hypertensive encephalopathy 13. History of stroke or transient ischemic attack within 6 months prior to study enrollment 14. Inadequately controlled hypertension (defined as systolic blood pressure of 150/100 mmHg on antihypertensive medications) (patients with treated hypertension are eligible) 15. Significant vascular disease (e.g., aortic aneurysm, aortic dissection, peripheral vascular disease) 16. History of organ allograft 17. Presence of grade \> 2 hepatic encephalopathy (see Appendix D) 18. Current, recent (within 4 weeks of the first infusion of this study), or planned participation in an additional experimental drug 19. Evidence of bleeding diathesis or coagulopathy or on warfarin. Note: If a patient has been on coumadin for a period of 1 month and has been stable, they may be accepted into the protocol. 20. Presence of clinically evident central nervous system or brain metastases 21. Major surgical procedure, open biopsy, or significant traumatic injury within 28 days prior to Day 1, anticipation of need for major surgical procedure during the course of the study 22. Vascular anatomy that precludes catheter placement or injection of LC Bead microspheres 23. Presence of collateral vessel pathways potentially endangering normal territories during embolization 24. Pregnant (positive pregnancy test) or lactating 25. Inability to comply with study and/or follow-up procedures 26. Life expectancy of less than 12 weeks 27. Child B8, B9 and C 28. ECOG ≥ 2 29. Patients with concomitant HIV infection or AIDS-related or serious acute or chronic illness 30. Presence of porto-systemic shunt 31. Severe atheromatosis 32. Substance abuse, medical, psychological or social conditions that may interfere with the patient's participation in the study or evaluation of study results 33. Active clinically serious infections (\>grade 2) 34. Patients receiving therapy for hepatitis A, B, or C. 35. Patients with obvious and/or symptomatic extrahepatic disease. Findings of uncertain significance, such as lung lesions less than 10 mm in diameter or enlarged periportal lymph nodes will not exclude patients, however, findings highly suspicious for metastatic HCC will exclude patients from this study. 36. Any contraindication for an arterial procedure such as impaired clotting tests (platelet count \< 50.000/mm3 or prothrombin activity \< 50 percent) 37. Any contraindication for systemic chemotherapy administration (serum bilirubin \> 3mg/dL, leukocyte count \< 3.000 cells/mm3) 38. Any contraindication for sorafenib administration