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 Patients" (in written consent form)
Exclusion Criteria:
* Current, known extra-hepatic tumors that, in the investigator's medical opinion, are likely to result in significant morbidity or mortality within the next 16 weeks.
* Pregnant or nursing an infant
* Known infection with HIV
* Clinically significant active infection or uncontrolled medical condition considered high risk for investigational new drug treatment
* Significant immunodeficiency due to underlying illness (e.g. hematological malignancies, congenital immunodeficiencies and/or HIV infection/AIDS) and/or medication (e.g. high-dose systemic corticosteroids)
* History of exfoliative skin condition (e.g. severe eczema, ectopic dermatitis, or similar skin disorder) that at some stage has required systemic therapy
* Clinically significant and/or rapidly accumulating ascites, peri-cardial and/or pleural effusions
* Liver tumors in a location that would potentially result in significant clinical adverse effects if post-treatment tumor swelling were to occur (e.g. tumors impinging on the biliary tract that could affect drainage)
* Severe or unstable cardiac disease
* Current, known CNS malignancy
* Anti-cancer therapy (e.g. RFA, TACE, PEIT, radioembolization, chemotherapy, surgery, or an investigational drug, etc.) within 4 weeks prior to first treatment
* Absolute contraindication to undergoing MRI scanning
* Experienced a severe systemic reaction or side-effect as a result of a previous smallpox vaccination
* Use of anti-platelet or anti-coagulation medication
* Use of the following anti-viral agents: ribavirin, adefovir, cidofovir (within 7 days prior to the first treatment), and PEG-IFN (within 14 days prior to the first treatment).
* Inability or unwillingness to give informed consent or comply with the procedures required in the protocol
* Patients with household contacts who meet any of these criteria unless alternate living arrangements can be made during the patient's active dosing period and for 7 days following the last dose of study medication:
* Pregnant or nursing an infant
* Children \< 12 months old
* History of exfoliative skin condition that at some stage has required systemic therapy
* Significant immunodeficiency due to underlying illness (e.g. HIV/AIDS) and/or medication
