A Study of Recombinant Vaccinia Virus to Treat Unresectable Primary Hepatocellular Carcinoma

Inclusion Criteria * Histological confirmation or clinical/laboratory diagnosis of primary hepatocellular carcinoma (HCC) * Cancer is not surgically resectable for cure * Child Pugh A or B * Tumor progression during or after at least one prior HCC treatment regimen (Note: If standard HCC therapies are either medically contraindicated or patient has refused those treatments, the patient may be eligible for this study) * Performance Score: KPS score of ≥ 70 * Anticipated survival of at least 16 weeks * Total bilirubin ≤ 2.5 x ULN * AST, ALT \< 5.0 x ULN * WBC \> 2,500 cells/mm3 and \< 50,000 cells/mm3 (GCSF treatment allowed) * ANC \> 1,250 cells/mm3 (GCSF treatment allowed) * Hemoglobin ≥ 9 g/dL (RBC transfusion allowed) * Platelet count ≥ 50,000 plts/mm3 * Acceptable coagulation status: INR ≤ 1.5 x ULN * Acceptable kidney function: Serum creatinine \< 2.0 mg/dL * If patients are diabetic or have a screening random glucose \> 160 mg/dL, a fasting glucose must be done and patients must be WNL or Grade 1 in order to be eligible for the study * For patients who are sexually active: able and willing to abstain from sex during treatment period and for 3 weeks following treatment, and use an acceptable method of birth control for 3 months after last injection with JX-594 * Able/willing to sign an IRB/IEC/REB-approved written consent form * Able and willing to comply with study procedures and follow-up examinations, including compliance with the "Infection Control Guidelines for Pat…