Inclusion Criteria: - Participants must have hepatocellular cancer (HCC) as confirmed by: histopathologic findings or by the finding of a liver tumor with arterial hypervascularization on contrast-enhanced computed tomography (CT) or magnetic resonance imaging and a serum alpha-fetoprotein (AFP) value exceeding 400ng/mL (European Association for the Study of Liver criteria for the diagnosis of hepatocellular carcinoma) - All stages of HCC are allowed, including patients with distant metastases. Patients may have multiple liver lesions as long as one lesion meets criteria - Patients may be liver transplant candidates. - Participants must have at least one tumor (index tumor) which can be accurately measured as 3.5-7cm in diameter (longest diameter to be recorded) on baseline imaging multi-phasic CT performed within 2 weeks of trial entry. See section 11 for the evaluation of measurable disease. - No prior therapy for the index hepatic tumor(s) being considered for radiofrequency ablation - No prior systemic treatment for HCC within 4 weeks prior to study entry. In addition, no prior anti-VEGF therapy allowed within 8 weeks prior to study entry. - Age 18 years or older. Because no dosing or adverse event data are currently available on the use of sorafenib in participants <18 years of age, children are excluded from this study but will be eligible for future pediatric Phase II trials. - Life expectancy > 8 weeks. - Eastern Cooperative Oncology Group performance status 0 or 1. (See appendix for definition) - RFA treatment must be clinically indicated for index tumor. Specifically, patients must not be candidates for surgical resection of the index tumor and clinical benefit must be anticipated by the primary physician from liver-direct treatment of the index tumor. - Participants must have acceptable overall RFA procedure risk: adequate cardiovascular, and functional status as specifically detailed in eligibility and exclusion criterion, acceptable intravenous sedation or general anesthesia risk and be able to lie flat for the procedure - Participants must have acceptable RFA procedure technique risk: the tumor must have adequate distance from adjacent vasculature and other organs to permit safe application of RFA (generally, less than a less than a 2.5cm clearance of the RF electrode from any vital structure such as the bowel, inferior vena cava, or aorta). The safety of the electrode placement will be made an attending radiologist experienced in RFA based on imaging studies. - 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 correctable to ≥ 50,000/mm3 Total bilirubin ≤ 1.5 times upper limit of normal (ULN) ALT and AST ≤ 5 x ULN Creatinine ≤1.5 times ULN or estimated glomerular filtration rate GFR ≥ 45 mL/min/m2 INR correctable to ≤ 1.5 or a PT/PTT correctable to 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. However, heparin or warfarin must be held prior to RFA as per standard of care such that the above criteria are met. - Ability to take oral medication and no evidence of impaired absorption. - The effects of sorafenib on the developing human fetus are unknown. For this reason and because anti-cancer agents are known to be teratogenic, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation and 2 weeks after the end of sorafenib treatment. Should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately. In addition, women may not be breast feeding during the time period of the study. - Women of childbearing potential must have a negative serum pregnancy test performed within 7 days prior to the start of treatment. - 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. Exclusion Criteria: - Participants who are anticipated to require treatment of the index treatment sooner than permitted by the nine day neoadjuvant course of sorafenib. - Participants who have had chemotherapy or radiotherapy within 4 weeks prior to entering the study or those who have not recovered from adverse events due to agents administered more than 4 weeks earlier. Participants currently receiving any other study agents. - Participants with known brain metastases should be excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events. - History of allergic reactions attributed to compounds of similar chemical or biologic composition to sorafenib. - Participants receiving any medications or substances that are inducers of CYP3A4 are ineligible because systemic sorafenib exposure may be decreased: rifampicin, St. John's wort, phenytoin, carbamazepine, Phenobarbital and dexamethasone. In addition, participants should not be receiving compounds that are metabolized/eliminated by predominantly UGT1A1 pathway (irinotecan) or CYP2B6 and CYP2C8 as systemic exposure may be increased. - Participants who exhibit any of the following conditions at screening will not be eligible for admission into the study. - Advanced liver disease (Child-Pugh C). (See appendix for definition of Child-Pugh classes) - Uncontrolled hypertension defined as systolic blood pressure > 150 mmHg or diastolic pressure > 90 mmHg, despite optimal medical management. - 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. (CTAE=Common Terminology Criteria for Adverse Events (CTCAE v3.0) which is available at http://ctep.cancer.gov/reporting//ctc.html). - 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 of severe or uncorrectable 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). - Any condition that impairs ability to swallow whole pills. - Any malabsorption problem. - The index tumor was treated with RFA or other treatment in the past. - Contraindication to or inability to undergo the RFA procedure, including adequate sedation and analgesia during the procedure. Contraindication to intravenous sedation or general anesthesia will be determined by Pre-Admission evaluation by the Department of Anesthesiology as per institutional standard of care. - Contraindication to or inability to undergo imaging with MRI (Pacemaker, MRI incompatible metal implant, Recently implanted vascular clip, history of claustrophobia not controlled with mild anxiolytic, metal fragment within the eye) - Uncontrolled intercurrent illness including, but not limited to ongoing or serious active infection (> CTCAE Grade 2), symptomatic congestive heart failure (> class II NYHA), unstable or new (<3 months) angina pectoris, recent myocardial infarction (within the past 6 months), cardiac arrhythmia (uncontrolled), or psychiatric illness/social situations that would limit compliance with study requirements. - Pregnant women are ineligible for this study because sorafenib is an anti-cancer agent with the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk of adverse events in nursing infants secondary to treatment of the mother with sorafenib, breastfeeding should be discontinued if the mother is treated with sorafenib. - Individuals with a history of a different malignancy are ineligible except for the following circumstances. Individuals with a history of other malignancies are eligible if they have been disease-free for at least 5 years and are deemed by the investigator to be at low risk for recurrence of that malignancy. 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 are ineligible because of the potential for pharmacokinetic interactions with sorafenib. In addition, these individuals are at increased risk of lethal infections when treated with marrow-suppressive therapy. Appropriate studies will be undertaken in participants receiving combination antiretroviral therapy when indicated.