This is a randomized, double-blind, placebo-controlled, parallel-group, multi-center study of vicriviroc maleate in HIV subjects infected with dual/mixed CCR5/CXCR4-tropic virus and who have documented resistance to at least 2 of the 3 antiretroviral drug classes (NRTI, NNRTI or PI) or at least 6 months experience with at least 2 of the following: one NRTI, one NNRTI, or one PI (excluding low-dose ritonavir) and failure on their current stable regimen. The study will compare the virologic benefit of adding vicriviroc to an optimized background regimen to a control group receiving placebo plus the new optimized background therapy. The optimized background regimen will be chosen by the investigator based on results of drug susceptibility tests performed at Screening, history of prior antiretroviral drug use by the patient, and drug toxicity. Primary efficacy analysis will be conducted when all subjects have completed 48 weeks of treatment. An interim analysis will be performed when all subjects have completed 24 weeks of treatment. Subjects who complete 48 weeks of treatment, or who discontinue early but are deemed eligible upon rescreening, will be offered participation in the open-label segment of the study, and will receive vicriviroc 30 mg once daily, if appropriate, until commercially available or until the sponsor terminates the clinical development of vicriviroc.