STA-9090 works by inhibiting the function of a protein in tumor cells called Hsp90. Hsp90 is thought to play a role in tumor growth. By interfering with this protein's function, STA-9090 may help kill tumor cells. This drug has been used in other research studies and information from those studies suggests that this agent may help to slow tumor growth in HCC.

The purpose of this research study is to find the highest dose of STA-9090 that can safely be given to participants with advanced HCC. The investigators will also get more information about the safety of STA-9090 and perform tests to learn more about how STA-9090 affects the body.

Study treatment is given in 4-week time periods called cycles. Patients will receive ST-9090 once weekly for the first 3 weeks of each cycle and no treatment on the fourth week. STA-9090 will be given by intravenous (IV) infusion. IV infusions occur through an IV catheter (or tube) placed in the vein. Each infusion will last about 60 minutes.

During each cycles patients will have blood tests, pregnancy test, and EKG. Twenty to thirty days after the last dose, patients will return for a physical exam, blood tests, urine test, EKG, and CT or MRI of chest and abdomen.

Inclusion Criteria:

• Histologically or cytologically confirmed hepatocellular carcinoma
• Measurable disease
• Life expectancy greater than 3 months
• ECOG performance status 0 or 1
• BCLC Stage C disease
• Lab values must be within limits outlined in protocol
• Child-Pugh score </= 6
• CLIP score 0-3
• Must agree to use adequate contraception

Exclusion Criteria:

• Chemotherapy or radiotherapy within 4 weeks prior to entering study or not recovered from adverse events due to agents administered more than 4 weeks earlier
• Receiving any other investigational agent
• Known brain metastases unless treated and radiographically and clinically stable without steroid or anticonvulsant medications for at least 4 weeks prior to first dose of STA-9090
• History of allergic reactions attributed to compounds of similar chemical or biologic composition to STA-9090
• Surgery, radiotherapy, or lesion ablative procedure to the only area of measurable disease
• Major surgery within 4 weeks prior to first dose of STA-9090
• Poor venous access for study drug administration or would require a peripheral or central indwelling catheter for study drug administration
• History of severe allergic or hypersensitivity reactions to excipients (e.g., Polyethylene glycol [PE] 300 and Polysorbate 80)
• Baseline QTc > 450 msec or previous history of QT prolongation while taking other medications
• Ventricular ejection fraction \