This is an open-label study that investigates the impact of a dose ramp-up strategy for sorafenib in patients with HCC. Clinical trial and post-marketing data suggest that sorafenib dose reductions and discontinuations due to adverse events are common and limit the drug's effectiveness. It is our hypothesis that a dose escalation strategy for sorafenib will improve the tolerability and allow a greater percentage of patients to remain on drug. The primary end-point of the study is the total accumulated and median daily dose of sorafenib delivered at month 2 and 4.