HIV-1 Specific T -Cells (HST-NEETs) for HIV-Infected Individuals

Inclusion Criteria: Recipient Inclusion Criteria for cell procurement and cell infusion: * ≥ 18 years and \< 65 years of age * Confirmation of HIV-1 infection \- any licensed ELISA test kit which is confirmed by Western blot or Multispot HIV-1/HIV-2 assay prior to screening. HIV culture, HIV antigen, plasma HIV RNA, or a second antibody test by a method other than ELISA is acceptable as an alternative confirmatory test. * On potent antiretroviral therapy, defined as at least 2 nucleoside/nucleotide reverse transcriptase inhibitors plus a non-nucleoside reverse transcriptase inhibitor, integrase inhibitor, or a protease inhibitor without interruption (Interruption is defined as missing doses by self report for no more than two (2) consecutive days or more than four (4) cumulative days) in the 12 weeks prior to cell procurement for HST NEETs manufacturing. Other potent fully suppressive antiretroviral combinations will be considered on a case- by-case basis. Prior changes in or elimination of medications for easier dosing schedule, intolerance, toxicity, or other reasons are permitted if an alternative suppressive regimen was maintained under the compliance criteria above. * Stable ART regimen for minimum of 12 weeks with no detectable HIV RNA concentrations as defined above. Participants may have had one or more changes in their ART regimen during the 12 week for tolerance, or dosing simplification. * Ability and willingness of participant to continue and be compliant with cART throughout the study. * Plasma HIV-1 RNA below detectable limit by conventional CLIA approved assays (\<50 copies/mL) for ≥ 1 year. A single unconfirmed plasma HIV RNA \> limit of detection but \< 1000 c/mL is allowed within the 12 months prior to screening/cell donation but none in the preceding 6 months, is permitted provided that a repeat RNA was \< 20. * Plasma HIV-1 RNA \< 50 copies/mL at screening. * CD4+ cell count \> 350 cells/mm3 at screening. * Karnofsky score of ≥ 50% * No active HCV infection (measureable HCV RNA) within 90 days of cell procurement. * No active HBV infection (measureable HBV DNA or HBVsAg+) within 90 days of cell procurement. * All female participants participating in sexual activity that could lead to pregnancy must agree to use at least two of the following reliable methods of birth control (at least one of which is a barrier method) for at least 21 days prior to study entry, continuing and until 12 weeks after the last dose of the study product: condoms (male or female) with or without a spermicidal agent, diaphragm or cervical cap with spermicide, Intrauterine Device, hormone-based contraceptive, tubal ligation, NuvaRing. * All male participants participating in sexual activity that could lead to pregnancy must agree to use condoms for at least 21 days prior to study entry, continuing and until 12 weeks after the last dose of the study product. * Ability and willingness of subject to give written informed consent. * Ability and willingness to provide adequate locator information and contact information for at least 2 adults who can reach the participant within 24 hours * Ability and willingness to communicate effectively with study personnel; considered reliable, willing, and cooperative in terms of compliance with the Protocol requirements. * Adequate vascular access (peripheral and central) for HST-NEET infusion. Exclusion Criteria: * Prior use of any HIV immunotherapy or vaccine within 12 months prior to Screening. * Use of any of the following within 90 days prior to entry: immunomodulatory, cytokine, or growth stimulating factors such as systemic corticosteroids, cyclosporine, methotrexate, azathioprine, anti-CD25 antibody, IFN, interleukin-2 (IL-2), Coumadin, warfarin, or other Coumadin derivative anticoagulants. * Patients on a CCR5 inhibitor or an entry inhibitor are not eligible for participation in the study * Received any infusion blood product, immune globulin, or hematopoietic growth factors within 90 days prior to study entry. * History of malignancy, immunodeficiency other than HIV, or any other condition that would make the subject unsuitable for the study in the opinion of the performance site PIs. * Any active malignancy that may require chemotherapy or radiation therapy. * Any licensed or experimental non-HIV vaccination (e.g., hepatitis B, influenza, pneumococcal polysaccharide) within 4 weeks prior to study entry. * Inability to comply with study requirements, which could impact study integrity and/or safety.