I. To determine whether the combination of navitoclax and sorafenib induces apoptosis that can be detected by peripheral blood biomarker analysis. (Dose escalation cohort) II. To assess peripheral blood biomarkers and pharmacokinetics in a more homogenous population. (Dose expansion cohort) III. To determine whether treatment is associated with Mcl-1 down regulation in hepatocellular carcinoma (HCC) at the maximum tolerated dose (MTD). (Dose expansion cohort) IV. To assess in a preliminary fashion whether pretreatment tumor cell levels of Mcl-1 predict response to this regimen through serial biopsies. (Dose expansion cohort)