This is a limited-center, open-label dose escalating phase I/IIa study of autologous T cells expressing LVgp120duoCAR molecules in people with HIV infection. It will follow a 3+3 design. Dose escalation decisions will be made when a minimum of three participants have completed the safety-evaluation period (45 days) at a given dose level. Cohort 1 will undergo infusion of a single low-dose regimen of LVgp120duoCAR-T cells. Cohort 2 will undergo non-ablative conditioning with cyclophosphamide, followed by infusion of a single low-dose regimen of LVgp120duoCAR-T cells. Cohort 3 will undergo non-ablative conditioning with cyclophosphamide, followed infusion of a single high-dose regimen of LVgp120duoCAR-T cells. Following administration of the experimental therapy, HIV medications will be paused for participants in each group during an analytic treatment interruption.

A limited-center, open-label dose escalating phase I/IIa study of autologous T cells expressing LVgp120duoCAR molecules will be performed. Participants will be enrolled sequentially in up to three cohorts following a 3+3 design. Dose escalation decisions will be made when a minimum of three participants have completed the safety-evaluation period (45 days) at a given dose level. No dose escalation will be allowed in an individual participant, and participants who have dose limiting adverse events will reinstate ART therapy at first available opportunity.

Following a 3+3 design, each cohort will enroll at least 3 participants. If there are no safety issues with dosing in a cohort, the investigators will proceed to the following cohort. If one participant in a cohort experiences a safety issue, an additional 3 individuals will be enrolled in that cohort to assess safety prior to proceeding to the next cohort. See below for Dose Escalation Procedures.

The first 3 participants start at Cohort 1. Data from Cohort 1 will be submitted for FDA review prior to dosing Cohorts 2 and 3 to determine if cyclophosphamide conditioning is needed.

Cohort 1: Participants will NOT undergo non-ablative conditioning with cyclophosphamide. A single dose of 3 x 105 cells/kg LVgp120duoCAR-T cells will be infused. ART will be interrupted immediately after infusion.

Cohort 2: Participants will undergo non-ablative conditioning with cyclophosphamide. A single dose of 3 x 105 cells/kg LVgp120duoCAR-T cells will be infused. ART will be interrupted immediately after infusion.

Cohort 3: Participants will undergo non-ablative conditioning with cyclophosphamide. A single dose of 1 x 106 cells/kg LVgp120duoCAR-T cells will be infused into the participant. ART will be interrupted immediately after infusion.

Dose Escalation Procedures:

1. If, after 45 days of study treatment, no participant out of the initial 3 in a cohort exhibits a study treatment-related DLT, then the next cohort of participants will be treated at the subsequent cohort.
2. If, after 45 days of study treatment, 1 participant out of the initial 3 in a cohort exhibits a study treatment-related DLT, then up to 3 additional participants will be added at that dose level.
3. If no additional participant develops a study treatment-related DLT (i.e., 1/6 participants with DLT at that dose level), then the next cohort of participants will be treated at the next higher dose level.
4. However, if a second participant develops a study treatment-related DLT, even if it is before there are 6 total participants on that level, then the maximum tolerated dose (MTD) has been exceeded and no additional participants should be added to this or any higher doses. A total of 6 participants should then be treated on the next lowest dose level to ensure its tolerability and to better define the MTD. Thus, the MTD is defined as the highest assigned dose level at which < 2/6 participants have a DLT.
5. If 2 participants in Cohort 1 experience a related DLT, the MTD will have been exceeded and no additional participants will be added at any higher level.
6. If the investigators experience DLTs in Cohort 1, the investigators will de-escalate the dose to 1 x 10^5 cells per kg. If the investigators experience DLTs at the de-escalated dose of 1 x 10^5 cells per kg, the study will stop.

Inclusion Criteria:

• Male or female, age ≥ 18 and ≤ 65 years
• HIV-1 infection
• On continuous antiretroviral therapy for at least 12 months without any interruptions of greater than 14 consecutive days, and on a stable regimen that does not include a non-nucleoside reverse transcriptase inhibitor (NNRTI) for at least 4 weeks or any long-acting ART drug that may be active in the participant after ART interruption for up to one year, without plans to modify ART during the study period
• Screening plasma HIV RNA levels below the limit of quantification on all available determinations in past 12 months (isolated single values ≥ 40 but < 200 copies/mL will be allowed if they were preceded and followed by undetectable viral load determinations)
• CD4+ T cell count nadir > 300 cells/mm3
• Screening CD4+ T-cell count ≥ 500 cells/mm3
• Available ART treatment history and the capacity to construct an effective antiretroviral treatment regimen
• Willing to pause ART as part of the study

Exclusion Criteria:

• Pregnant, breastfeeding, or unwilling to practice birth control during participation in the study
• ART regimen that includes a long-acting anti-HIV drug and/or NNRTI that may be active in the participant for up to one year after ART interruption
• ART regimen that includes protease inhibitor(s) and/or AZT. These drugs may increase the toxicity of cyclophosphamide.
• Any history of an HIV-associated malignancy, including Kaposi's sarcoma and any type of lymphoma, or virus-associated cancers
• History of or current active hepatitis B (HBV) infection defined as positive HBV surface antigen test. A positive anti-HBc regardless of HBsAg status.
• Active hepatitis C (HCV) infection
• Active or latent tuberculosis infection
• Chronic liver disease
• Active and poorly controlled atherosclerotic cardiovascular disease
• Unwillingness to abstain from sex or use barrier protection for any sexual activity during the treatment interruption.