This is a phase I/II dose escalation study designed to examine the safety, pharmacokinetics, and antiviral activity of AMD-3100 in successive cohorts of HIV-infected patients. Each cohort will consist of 4 patients. The initial dose will be 2.5 mg/kg/hr administered by continuous intravenous infusion for 10 consecutive days. Additional cohorts of 4 patients each will receive AMD-3100 by intravenous infusion at two-fold higher doses unless grade 3 or 4 adverse events occur in one or more patients within a dose cohort A reduction in plasma viral load > one log in >2 patients in a cohort will be considered evidence of promising antiviral activity. If this criterion is met, and the drug is tolerated, additional cohorts (doubling the dose) will be enrolled to determine whether there is a dose response relationship for antiviral activity. If evidence of nonlinear pharmacokinetics develops at higher doses, dose escalation will cease until a full evaluation of the data is performed and discussed with the FDA reviewers.