This study is for people with cancer of the liver that cannot be completely removed by surgery. This study involves giving the drugs mitomycin-C and cisplatin, into an artery in the liver. Mitomycin-C is a drug that has been approved by the FDA to treat cancer of the stomach and pancreas. Mitomycin-C is a drug that causes cancer cells to die and prevents them from reproducing. Cisplatin is also a drug that has been approved by the FDA. Cisplatin is approved to treat cancer of the testes, ovaries, lung, esophagus, bladder, head and neck. Cisplatin is a drug that prevents cancer cells from reproducing. The purpose of this study is to see how long it takes subjects' tumor(s) to grow after receiving the study drugs. Another purpose of this study is to look at the side effects of this study therapy and how long subjects survive after receiving it.

An additional purpose of this study is to see how well we can predict subjects' response to the study therapy, based on blood and tumor tissue tests. These tests will measure the levels of genes (the cell's blueprint) in subjects' tumors and blood. These genes affect how people's bodies react to the cancer drugs.

Inclusion Criteria:

• Unresectable, histologically confirmed hepatocellular carcinoma with evident disease limited to liver.
• Tissue from tumor must be available. This may be paraffin embedded tissue from previous biopsy/resection or if it is not available, a repeat biopsy must be performed. The requirement for biopsy may be waived if alpha-fetoprotein is greater than 500 ng/mL and in the investigators opinion not explained by a concurrent hepatic inflammatory process.
• Patients must agree to have a 20 cc blood sample drawn in addition to routine labs with each cycle of chemotherapy.
• Patients must have measurable disease. If prior radiation therapy was administered, measurable disease must be outside the radiation field.
• Patients must have a Zubrod performance status of 0-2.
• Patients must have a predicted life expectancy of at least 12 weeks.
• Patients must have a pre-treatment granulocyte count (i.e., segmented neutrophils + bands) of greater than or equal to 1,500/mm3, a hemoglobin level of greater than or equal to 9 gm/dl, and platelet count greater than or equal to 50,000/mm3. The granulocyte requirement may be waived if in the investigator's opinion the lower count reflects hypersplenism with adequate bone marrow reserves.
• Patients must have adequate renal function as documented by a calculated creatinine clearance ≥ 60.
• Patients must have adequate hepatic function as documented by a serum bilirubin less than or equal to 2x the institutional upper limit of normal, regardless of whether patients have liver involvement secondary to tumor. Patients may not have ascites or the ascites must be responsive to diuretics.

Exclusion Criteria:

• Patients who have received prior chemotherapy for unresectable disease
• Patients with any active or uncontrolled infection, including known HIV infection. (Patients with active hepatitis B will be placed on lamivudine. Patients with active hepatitis C will be eligible if liver tests qualify (5.1.9)
• Patients with psychiatric disorders that would interfere with consent or follow-up. Pregnant or lactating women. Men and women of reproductive potential may not participate unless they have agreed to use an effective contraceptive method.
• Patients with any other severe concurrent disease, which in the judgment of the investigator, would make the patient inappropriate for entry into this study.

Up to 1 year

Adverse events are assessed during regularly scheduled follow up.