A Phase II Clinical Trial to Study the Efficacy and Safety of Pembrolizumab (MK-3475) in Subjects with High Risk Non-muscle Invasive Bladder Cancer (NMIBC) Unresponsive to Bacillus Calmette-Guerin (BCG) Therapy.

Inclusion Criteria: - Histologically-confirmed diagnosis of high risk non-muscle-invasive (T1, high grade Ta and / or carcinoma in situ [CIS]) transitional cell carcinoma of the bladder (mixed histology tumors allowed if transitional cell histology is predominant histology). - Fully resected disease at study entry (residual CIS acceptable) - BCG-unresponsive high risk non-muscle-invasive bladder cancer after treatment with adequate BCG therapy - Ineligible for radical cystectomy or refusal of radical cystectomy - Available tissue from a newly obtained core biopsy of a tumor lesion not previously irradiated - Eastern Cooperative Oncology Group (ECOG) performance status of 0, 1, or 2 - Adequate organ function - Female participants of childbearing potential have a negative urine or serum pregnancy test and must be willing to use an adequate method of contraception - Male participants must be willing to use an adequate method of contraception Exclusion criteria: - Centrally assessed muscle-invasive, locally advanced nonresectable, or metastatic urothelial carcinoma (i.e., T2, T3, T4, and / or stage IV) - Centrally assessed concurrent extra-vesical (i.e., urethra, ureter, or renal pelvis) non-muscle invasive transitional cell carcinoma of the urothelium - Currently participating or has participated in a study of an investigational agent and received study therapy or received investigational device within 4 weeks prior to the first dose of study treatment - Received intervening intravesical chemotherapy or immunotherapy from the time of most recent cystoscopy / Transurethral Resection of Bladder Tumor (TURBT) to starting study treatment - Received prior chemotherapy, targeted small molecule therapy, or radiation therapy within 2 weeks prior to starting study treatment or not recovered from adverse events due to a previously administered agent - Known additional malignancy that is progressing or requires active treatment excepting basal cell carcinoma of the skin, squamous cell carcinoma of the skin that has undergone potentially curative therapy or in situ cervical cancer. A history of prostate cancer that was treated with definitive intent (surgically or through radiation therapy) is acceptable provided that the following criteria are met: Stage T2N0M0 or lower; Gleason score ≤7 and prostatic-specific antigen (PSA) undetectable for at least 1 year while off androgen deprivation therapy that was either treated with definitive intent or untreated in active surveillance that has been stable for the past year prior to study allocation - Active autoimmune disease that has required systemic treatment in the past 2 years - Evidence of interstitial lung disease or active non-infectious pneumonitis - Active infection requiring systemic therapy - Pregnant or breastfeeding, or expecting to conceive within the projected duration of the trial through 120 days after the last dose of study treatment - Prior therapy with an anti-programmed cell death 1 (PD-1), anti-PD-ligand 2 (L2) agent, or with an agent directed to another co-inhibitory T-cell receptor - Known human immunodeficiency virus (HIV) - Known active Hepatitis B or C infection - Received a live virus vaccine within 30 days of planned start of study treatment - Has had an allogeneic tissue/solid organ transplant