Autologous CD4 T-Cells in HIV (C34-CXCR4)

Inclusion Criteria: * HIV-1 infection, documented by any licensed rapid HIV test or HIV enzyme or chemiluminescence immunoassay (E/CIA) test kit at any time prior to enrollment and confirmed by a licensed Western blot or a second antibody test by a method other than the initial rapid HIV and/or E/CIA, or by HIV-1 antigen, plasma HIV-1 RNA VL. * Ability and willingness of subject to provide informed consent. * Men and women ages ≥18 years. * Clinically stable on their first or second HAART regimen. Changes while the patient HIV viral load is undetectable does not count toward the number of ART regimens used, only changes made for virologic failure (for example an individual switching from an NNRTI-based regimen to an integrase inhibitor based regimen while the HIV viral load is undetectable will still be in their first regimen). Site investigator anticipates that a fully active alternative ART regimen could be constructed in the event of virologic failure on the current ART regimen.The current regimen should have no changes within 4 weeks of enrollment. Subjects must be willing to continue on current antiretroviral therapy for the duration of the study except for the duration of the 16 week analytical treatment interruption. (NOTE: changes to safely begin the treatment interruption are permitted). * Screening HIV-1 RNA that is ≤50 copies/mL using a FDA-approved assay performed by any laboratory that has a CLIA certification or its equivalent within 30 days prior to enrollment. * HIV-1 RNA ≤50 copies/mL using a FDA-approved assay for at least 24 weeks prior to enrollment performed by any laboratory that has a CLIA certification or its equivalent. * NOTE: HIV-RNA must be measured at least once in the last 24 weeks and at least 3 days before the screening measure. Single determinations that are between \>50 and \<400 copies/mL (ie, blips) are allowed as long as the preceding and subsequent determinations are ≤50 copies/mL. The screening value may serve as the subsequent determination ≤50 copies/mL following a blip * NOTE: subjects who have participated in other trials using ATI's will be permitted since detectable virus during the interruption does not represent virologic failure. These subjects should have at least 24 weeks of VL \<50 copies/mL. * Screening CD4+ T-cell count ≥450 cells/ mm3 within 30 days of enrollment. * Started ART with nadir CD4+ ≥200 cells/ mm3. * The following laboratory values obtained within 30 days prior to enrollment meeting the following criteria: * Absolute neutrophil count (ANC) ≥1000 cells/mm3 * Hemoglobin:≥10.0(males); ≥9.5 (females) g/dL * Platelet count: 100,000/mm3 * Calculated creatinine clearance ≥50 mL/min estimated by the Cockcroft-Gault equation * Alanine aminotransferase (ALT) ≤ 2.0 x ULN * Negative HBsAg within 6 months prior to enrollment. * Negative HCV serology, or if positive, negative HCV RNA within 6 months prior to enrollment * Adequate venous access and no other contraindications for leukapheresis. * Have a Karnofsky Performance Score of 70 or higher. * Have a recorded viral load set point prior to starting antiretroviral therapy Exclusion Criteria: * Acute or chronic hepatitis B or hepatitis C infection * Current or prior AIDS diagnosis. * History of cancer or malignancy, with the exception of successfully treated basal cell or squamous cell carcinoma of the skin * History or any features on physical examination indicative of active or unstable cardiac disease or hemodynamic instability. * NOTE: Subjects with a history of cardiac disease may participate with a physician's approval. * History or any features on physical examination indicative of a bleeding diathesis * Have been previously treated with any HIV experimental vaccine within 6 months prior to enrollment, or any previous gene therapy using an integrating vector. * NOTE: Subjects treated with placebo in an HIV vaccine study will not be excluded if documentation that they received placebo is provided. * Use of chronic systemic corticosteroids, hydroxyurea, or immunomodulating agents (e.g., interleukin-2, interferon-alpha or gamma, granulocyte colony stimulating factors, etc.) within 30 days prior to enrollment. * NOTE: Recent or current use of inhaled steroids is not exclusionary. If subjects are prescribed a brief course of oral corticosteroids, the use should be limited to less than 7 days. Use of steroids before apheresis and immune assessment blood draws should be discouraged as it will affect white blood cell function. * Breast-feeding, pregnant, or unwilling to use acceptable methods of birth control. * Anticipated use of aspirin, dipyridamole, warfarin or any other medication that is likely to affect platelet function or other aspects of blood coagulation during the 2-week period prior to leukapheresis * Active drug or alcohol use or dependence that, in the opinion of the site investigator, would interfere with adherence to study requirements. * Serious illness requiring systemic treatment and/or hospitalization within 30 days prior to enrollment * Asymptomatic baseline serum chemistry elevations in LFTs, bilirubin, and serum creatinine due to HAART medication are not exclusionary, when in the opinion of the investigator, the abnormalities are not attributable to intrinsic hepatorenal disease. Such baseline elevations must be due to HAART. * Receipt of vaccination within 30 days prior to enrollment. * NOTE: It is recommended that subjects enrolling into this study should have completed their routine vaccinations (hepatitis A, hepatitis B, pneumococcus, and tetanus diphtheria booster) at least 30 days prior to enrollment * Have an allergy or hypersensitivity to study product excipients (human serum albumin, DMSO and Dextran 40).