The purpose of this study is to evaluate the effect of combining a new investigational drug (OSI-906) with a standard drug (sorafenib) on the control of liver cancer (hepatocellular cancer). Sorafenib (brand name Nexavar®) is a drug that is approved for the treatment of advanced liver cancer. It works by stopping the growth of new blood vessels around the tumor. OSI-906 is an investigational agent that works by inhibiting the effects of a growth hormone on the cancer. The safety and efficacy of combining OSI-906 and sorafenib in the treatment of liver cancer risk not known. The current study will confirm the safety of the combination in the first six patients and evaluate the activity of the combination in patients with advanced liver cancer.