Sorafenib Therapy Prior to Radiofrequency Ablation for Intermediate Sized Hepatocellular Cancer

Inclusion Criteria: * Confirmed hepatocellular cancer (HCC) by pathology or by NCCN imaging guidelines * All HCC stages are allowed. May be a liver transplant candidate. * At least one tumor (index tumor) accurately measured as 3.5-7cm in diameter (long and short axis diameter to be recorded, but only one needs to meet this criteria) on baseline imaging. * No prior therapy for the index tumor * No prior systemic treatment for HCC within 4 weeks and no prior anti-VEGF therapy within 8 weeks of study entry. * Life expectancy \> 8 weeks. * ECOG \>=0 or 1 * RFA clinically indicated for index tumor. * Acceptable overall RFA and anesthesia risk. * Adequate bone marrow, liver and renal function: Hemoglobin \>9.0 g/dl; Absolute neutrophil count (ANC)\>1,500/mm3; Platelet count correctable to \>50,000/mm3; compensated liver function (Child-Turcotte-Pugh A, B7 or B8); Creatinine \<1.5 times ULN; INR correctable to \<1.5. * Ability to take oral medication and no evidence of impaired absorption. Exclusion Criteria * Urgent treatment of the index tumor anticipated. * Participants who have not recovered from adverse events due to agents administered more than 4 weeks earlier. Participants currently receiving any other study agents. * Known brain metastases * History of allergic reactions attributed to compounds of similar chemical or biologic composition to sorafenib. * Participants receiving medications or substances that are inducers of CYP3A4 (rifampicin, St. John's wort, phenytoin, carbamazepine, phenobarbital and dexamethasone) or that are metabolized/eliminated by predominantly UGT1A1 pathway or by CYP2B6 and CYP2C8. * Decompensated liver disease * Uncontrolled hypertension * Thrombolic or embolic events within the past 6 months. * Hemorrhage/bleeding event within 4 weeks * Serious non-healing wound, ulcer, or bone fracture. * Evidence of severe or uncorrectable bleeding diathesis or coagulopathy * Major surgery, open biopsy or significant traumatic injury within 4 weeks of study entry. * Contraindication to or inability to undergo the RFA procedure, * Contraindication to or inability to undergo imaging with MRI * Uncontrolled intercurrent illness * Individuals with a history of a different malignancy unless disease-free for at least 5 years and are deemed by the Investigator to be at low risk for recurrence. Individuals with the following cancers are eligible if diagnosed and treated within the past 5 years: cervical cancer in situ, and basal cell or squamous cell carcinoma of the skin. * HIV-positive individuals on combination antiretroviral therapy For additional inclusion/exclusion criteria details contact Study Site.