The investigational product, ibalizumab, is a humanized IgG4 monoclonal antibody administered via intravenous infusion at 800 mg every 2 weeks or at 2000 mg every 4 weeks. In addition to study drug, all patients will receive an optimized background regimen (OBR), which is a standard-of-care regimen selected by the investigator prior to randomization that is comprised of 2-4 antiretroviral agents. These agents must have been approved by the local regulatory agency or be available through expanded-access programs for treatment of human immunodeficiency virus (HIV).