Intra-lesional Nivolumab Therapy for Limited Cutaneous Kaposi Sarcoma

Inclusion Criteria: 1. For screening: Participants must have histologically confirmed KS with active cutaneous disease and have less than 25 lesions. For enrollment: Participants must have histologically confirmed KS in the research skin biopsy performed during the screening visit. 2. Participants must have measurable cutaneous KS disease, defined as 1 or more marker lesion that is bi-dimensionally measurable, and \>=0.5cm in shortest dimension. These measurable lesions must not have received previous local radiation, surgical, or intralesional cytotoxic therapy that would prevent response assessment. Note: Participants may eligible even if some KS lesions that have previously been treated with local therapy, as long as other untreated KS lesions are measurable as defined in the protocol. 3. For the initial safety cohort (cohort A), participants have to be treatment-experienced, i.e. at least one of the KS skin lesions has been persisted despite having been treated with: * systemic chemotherapy; OR * 1 or more topical therapy, local radiation, surgery, or intra-lesional cytotoxic therapy. For the expansion cohort (cohort B), participants can be either treatment-experienced or treatment-naïve. For the extension cohort (cohort B-plus), participants are from the expansion cohort above (cohort B) who have achieved partial response (PR) or complete response (CR) in their injected KS lesion at week 26 or later. 4. Age \>= 18 years. 5. If human immunodeficiency virus (HIV)-infected, participants must have: * HIV-1 infection, documented by any federally approved, licensed HIV rapid test performed in conjunction with screening (or ELISA, test kit, and confirmed by Western blot or other approved test). Alternatively, this documentation may include a record demonstrating that another physician has documented the participant's HIV status based on either: 1) approved diagnostic tests, or 2) the referring physician's written record that HIV infection was documented, with supporting information on the participant's relevant medical history and/or current management of HIV infection * CD4 \>= 350 cells/mm3 * HIV-1 viral load below the limit of detection by commercial assays (\<75 copies/mL). * Participants MUST receive appropriate care and treatment for HIV infection, including antiretroviral medications when clinically indicated, and should be under the care of a physician experienced in HIV management. Participants should be documented to be on an effective combination anti-retroviral (ART) regimen, generally a 3-drug regimen based on Department of Health and Human Services (DHHS) treatment guidelines by a licensed health care provider. Participants will be eligible regardless of antiretroviral medication (including no antiretroviral medication) provided there is no intention to initiate therapy or the regimen has been stable for at least 4 weeks with no intention to change the regimen within 12 weeks following enrollment. 6. If HIV-uninfected, participants must have documentation of a negative HIV result by any federally approved, licensed HIV test within the last 12 months. 7. Adequate organ function defined as follows: 1. Leukocytes \> 3,000/microliter (mcL). 2. Absolute neutrophil count \> 1,000/mcL. 3. Hemoglobin \> 10 g/dL. 4. Platelets \> 100,000/mcL. 5. Total bilirubin within normal institutional limits. 6. Aspartate aminotransferase (AST)/serum glutamic-oxaloacetic transaminase (SGOT) \< 2.5 X institutional upper limit of normal (ULN) 7. Alanine aminotransferase (ALT)/ serum glutamic-pyruvic transaminase (SGPT) \< 2.5 X institutional ULN 8. Creatinine \< 1.5 X institutional ULN 8. Participants must be purified protein derivative (PPD) negative. Alternatively, the QuantiFERON-TB Gold In-Tube (QFT-GIT) assay (Cellestis Limited, Carnegie, Australia) can be used. An individual is considered positive for M. tuberculosis (TB) infection if the Interferon (IFN)-gamma response to TB antigens is above the test cut-off (after subtracting the background IFN-gamma response in the negative control). The result must be obtained within 12 months prior to enrollment. PPD positive (or QuantiFERON assay positive) participants are permitted if prophylaxis has been completed prior to enrollment. 9. Eastern Cooperative Oncology Group (ECOG) Performance Status of \<=1 (Karnofsky \>= 70%). 10. The effects of nivolumab on the developing fetus are unknown. Therefore, only the following patients should be enrolled: 1. Woman of child-bearing potential (WOCBP), defined as a sexually mature woman who has not undergone a hysterectomy (the surgical removal of the uterus) or bilateral oophorectomy (the surgical removal of both ovaries)) or, has not been naturally postmenopausal for at least 24 consecutive months (i.e., has had menses at any time during the preceding 24 consecutive months} must have negative serum pregnancy test within 7 days before starting study treatment in WOCBP and willingness to adhere to acceptable forms or birth control (a physician-approved contraceptive method (oral, injectable, or implantable hormonal contraceptive; tubal ligation; intra-uterine device; barrier contraceptive with spermicide; or vasectomized partner). WOCBP receiving nivolumab will be instructed to adhere to contraception for a period of 6 months after the last dose. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study (including the time after last dose previously mentioned), she (or the participating partner) should inform the treating physician immediately. 2. Men receiving nivolumab and who are sexually active with WOCBP will be instructed to adhere to contraception for a period of 7 months after the last dose of investigational product. Exclusion Criteria: 1. Prior systemic KS-directed treatments or investigational modalities \<= 5 half-lives or 4 weeks, whichever is shorter, prior to starting study drug or who have not recovered from side effects of such therapy to grade 1 or less. 2. Presence of any visceral KS (including KS-associated lymphedema) requiring systemic chemotherapy. This includes, but not limited to, any symptomatic visceral KS or asymptomatic pulmonary KS. 3. Hypersensitivity to nivolumab or any of its excipients. 4. Has a known additional malignancy that is progressing or requires active treatment. Exceptions include basal cell carcinoma of the skin or squamous cell carcinoma of the skin that has undergone potentially curative therapy or in situ cervical cancer. 5. Opportunistic infection within the last 3 months. 6. Has active autoimmune disease that has required systemic treatment in the past 2 years (i.e. with use of disease modifying agents, corticosteroids or immunosuppressive drugs). Replacement therapy (e.g. thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment. 7. Has received prior therapy with an anti-PD-1, anti-PD-L1, or anti-PD-L2 agent. This does not apply to participants in the extension cohort (cohort B-plus). 8. Active systemic immunosuppressive therapy. 9. The use of prednisone or equivalent 10mg or greater a day that cannot be discontinued with more than 7 consecutive days of steroids within the prior 2 weeks. 10. Prior organ allograft or allogeneic transplantation, if the transplanted tissue is still in place. 11. Unstable angina, significant cardiac arrhythmia, or New York Heart Association (NYHA) class 3 or 4 congestive heart failure. 12. Major surgery ≤ 2 weeks prior to starting a study drug or who have not recovered from side effects of such therapy. 13. Any significant medical condition, laboratory abnormalities, which places the subject at unacceptable risk if he/she were to participate in the study. 14. Any condition that confounds the ability to interpret data from the study.