In this second study in humans, DCR-MYC will be administered by 2 hour intravenous (IV) infusion, once weekly for 2 weeks followed by a rest week (3 weeks = 1 cycle), to patients with hepatocellular carcinoma who are either sorafenib-refractory, sorafenib-intolerant despite dose reduction and best supportive care, or for whom neither sorafenib nor other suitable therapy is available. During the Phase 1b portion of the study, the highest safe dose of DCR-MYC that can be administered will be identified. In addition, the pharmacokinetic (PK) profile, potential pharmacodynamic (PD) effects, as well as the preliminary antitumor activity of DCR-MYC will be evaluated. During the Phase 2 portion of the study, up to 30 patients will be treated at the MTD identified in Phase 1b in order to further evaluate safety and tolerability, as well as assess the antitumor activity, of DCR-MYC.