Trial of Sorafenib in Hepatocellular Cancer (HCC) Transplant Patients

Inclusion Criteria: * Age ≥18 years old * ECOG Performance Status 0-2 * Post liver transplant and have explants with histologically confirmed hepatocellular carcinoma. * No evidence of HCC disease at study entry by imaging * Eligible to start 4 weeks post transplant (29 days post transplant) as long as they are on stable doses of immunosuppressants. * "High risk" for recurrence after transplantation * Received prior surgical resection, chemoembolization or other local therapy prior to transplant. * Have Child-Pugh Class A or compensated Child-Pugh Class B liver dysfunction at the start of therapy * Have adequate bone marrow, liver and renal function as assessed by the following: * Hemoglobin ≥ 8.0 g/dl * Absolute neutrophil count (ANC) ≥ 1,500/mm3 * Platelet count ≥ 75,000/mm3 * Total bilirubin ≤ 1.5 times ULN * ALT and AST ≤ 5 x ULN * Creatinine ≤ 1.5 times ULN * Albumin ≥ 2.5 mg/dl * Women of childbearing potential must have a negative serum pregnancy test performed within 14 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. * Exhibit the ability to understand and willingness to sign a written informed consent regarding the study and alternative treatments. * INR \< 1.5 or a PT/PTT within normal limits. Exclusion Criteria: * Cardiac disease: Congestive heart failure \> class II NYHA. * 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. * Active clinically serious infection \> CTCAE Grade 2. * Thromboembolic events such as a cerebrovascular accident (including transient ischemic attacks) within the past 6 months. * Any hemorrhage/bleeding event ≥ CTCAE Grade 3 within 4 weeks of first dose of study drug. * Serious non-healing wound, ulcer, or bone fracture within 4 weeks of first dose of study drug. * Evidence or history of bleeding diathesis or coagulopathy within 4 weeks of first dose of study drug. * Major surgery, open biopsy or significant traumatic injury within 4 weeks of first study drug. * Use of St. John's Wort or rifampin within 4 weeks of first dose of study drug. * 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. * Patients who are pregnant or breastfeeding. Breastfeeding should be discontinued if the patient is to be treated. * Prior malignancy treated during the prior 5-years (other than localized non-melanoma carcinoma of the skin). * Any condition or social situation that may limit patient's compliance with the study regimen * Known brain metastasis. Patients with neurological symptoms must undergo a CT scan/MRI of the brain to exclude brain metastasis prior to enrollment. * Known human immunodeficiency virus (HIV) infection (hepatitis B and hepatitis C infection will not be exclusion criteria. * Pulmonary hemorrhage/bleeding event ≥ CTCAE Grade 2 within 4 weeks of first dose of study drug. * Any malabsorption problem which in the investigator's opinion would prevent adequate absorption of the sorafenib. * On M-Tor inhibitors