Ph1 Study of FT538 Alone and With Vorinostat for Persistent Low-Level HIV Viremia

Inclusion Criteria: * Male or female, age ≥18 and ≤65 years at the time of signing the consent form * HIV-1 infection on continuous antiretroviral therapy (ART) for at least 12 months without any interruptions of greater than 14 consecutive days and without plans to modify ART before the End of Treatment visit. * Two or more consecutive detectable HIV RNA levels of ≤200 copies/mL in the last 2 years, with at least one determination meeting this criterion in the previous 12 months. (If testing was not obtained within 42 days of planned dose 1, test will be repeated during subject screening to confirm status) * Screening CD4+ T cell count ≥350 cells/ µl within 28 days of the 1st dose of FT538. * Completion of initial COVID-19 vaccination series and/or documented COVID-19 infection with completion of treatment ≥ 3 months prior * Patient weight of ≥ 50 kg due to FT538 fixed cell dosing and FT538 product pre-dosed packaging. Adequate organ function within 14 days of Day 1, defined as the following: * Platelet counts \>150,000/mm\^3 * Hemoglobin \> 12.5 g/dL for men and \> 11.5 g/dL for women. It is not acceptable for patients to be transfused within the prior month to meet this requirement. The use of Epogen is permitted. * AST and ALT ≤ 3 x upper limit of institutional normal * Estimated CrCl (eGFR) \>50 mL/min/1.73m\^2 * Persons of childbearing potential or with partners of childbearing potential must be willing to abstain from heterosexual activity or to use a highly effective form of contraception from the time of study enrollment through at least 4 months after the last dose of FT538. Persons are considered of childbearing potential unless: they are postmenopausal; are surgically sterile; or they have a congenital or acquired condition that prevents childbearing. NOTE: Abstinence is acceptable if this is the usual lifestyle and preferred contraception. For Dose Cohort 4 (FT538 plus Vorinostat): * Females of childbearing potential must use highly effective contraception from the time of study enrollment through 6 months after the last dose of vorinostat. * Males with partners of childbearing potential must use highly effective contraception from the time of study enrollment through 3 months after the last dose of vorinostat or 4 months after the last dose of FT538, whichever is more conservative. * Must agree to and sign the consent for the Master Long-Term Follow-Up study to fulfill the FDA recommended 15 years following exposure to the investigational gene therapy product. * Voluntary written consent prior to the performance of any research related procedures. Exclusion Criteria: * Pregnant, breastfeeding, or unwilling to practice birth control for a minimum of 4 months after the last dose of FT538. If of childbearing potential, a negative pregnancy test is required within 14 days prior to the 1st dose of FT538 or within 7 days prior to the 1st dose of vorinostat if treated in Dose Cohort 4. * Known allergy to the following FT538 components: albumin (human) or DMSO. * Currently receiving or likely to require systemic immunosuppressive therapy (e.g., prednisone \>5 mg daily) for any reason within 5 days before the 1st dose of FT538 and 14 days after the last dose of FT538 - inhaled and topical steroids are permitted. * Active or recent malignancy requiring systemic chemotherapy or surgery in the preceding 36 months or for whom such therapies are expected in the subsequent 12 months - minor surgical removal of localized skin cancers (squamous cell carcinoma, basal cell carcinoma) is permitted. * Prior history of solid organ transplant or hematopoietic stem cell transplant. * Receipt of any investigational agent (not approved by the FDA for any indication) within 28 days prior to the first dose of FT538. Note that participation in prior HIV cure studies, including those involving IL-2 or N803, is permitted as long as experimental therapy completed \>28 days prior. * Chronic liver disease defined as Class B and C on the Child-Pugh scale. * Active and poorly controlled atherosclerotic cardiovascular disease (ASCVD), as defined by 2013 ACC/AHA guidelines, including a previous diagnosis of any of the following within the previous 12 months: (a) acute myocardial infarction, (b) acute coronary syndromes, (c) stable or unstable angina, (d) coronary or other arterial revascularization, (e) stroke, (f) transient ischemic attack (TIA), or (g) peripheral arterial disease presumed to be of atherosclerotic origin. * Moderate-severe obstructive lung disease. In subjects reporting a history of mild obstructive lung disease at screening, pulmonary function test (PFT) to be obtained and patient excluded from study if the FEV1 is \<80% of predicted. * Non-malignant CNS disease such as stroke, epilepsy, CNS vasculitis, or neurodegenerative disease or receipt of medications for these conditions in the 2-year period leading up to study enrollment. * Known concurrent or recent (defined as having received treatment within the last 3 months) infection with: * Latent or active TB infection prior to completing a standard regimen of anti-TB therapy; defined as meeting PPD criteria for TB exposure or a positive quantiferon gold test collected at screening * Active fungal infection requiring systemic antifungal therapy * Chronic active hepatitis B or C. For Hepatitis B this will be defined as HBs antigen + and for Hepatitis C this will be defined as Hepatitis C antibody positive and Hepatitis C PCR+. * COVID-19; defined as a positive SARS-CoV-2 PCR test at screening or a history of COVID-19 diagnosed within the last 3 months. * Clinical vaccination administered within 6 weeks of the 1st dose of FT538. * Presence of any social issues that, per investigator judgement, are likely to interfere with study conduct or may cause increased risk to patient. * Patient history of alcohol or substance abuse that, per investigator judgement, are likely to interfere with study conduct or may cause increased risk to patient * Any medical condition or clinical laboratory abnormality that, per investigator judgement, precludes safe participation in and completion of the study or that could affect compliance with protocol conduct or interpretation of results.