The purpose of this study is to evaluate pembrolizumab (MK-3475) in the treatment of participants with relapsed or refractory Classical Hodgkin Lymphoma. Participants will be randomized to receive either pembrolizumab or brentuximab vedotin for up to 35 three-week cycles of treatment.

The primary hypotheses of this study are that treatment with pembrolizumab prolongs Progression Free Survival (PFS) and Overall Survival (OS) in participants with relapsed or refractory Classical Hodgkin Lymphoma compared to treatment with brentuximab vedotin.

Inclusion Criteria:

• Has relapsed (disease progression after most recent therapy) or refractory (failure to achieve Complete Response (CR) or Partial Response (PR) to most recent therapy) classical HL and meets one of the following criteria:
  1. Has failed to achieve a response or progressed after autologous stem cell transplant (auto-SCT). Participants must not have had previous treatment with brentuximab vedotin.
  2. Is not an auto-SCT candidate due to: chemo-resistant disease (unable to achieve CR or PR to salvage chemotherapy), advanced age (≥65 years of age), or any significant coexisting medical condition (cardiac, renal, pulmonary, or hepatic dysfunction) likely to have a negative impact on tolerability of auto-SCT. Participants <65 years of age who refuse auto-SCT are not eligible for this study. Note: Sponsor review and approval of participants <65 years of age who are not auto-SCT candidates are required before randomization. Participants must have received at least 2 prior multi-agent chemotherapy regimens that did not include brentuximab vedotin.
• Has measureable disease defined as ≥1 lesion that can be accurately measured in at least 2 dimensions with spiral computed tomography (CT) scan. Minimum measurement must be >15 mm in the longest diameter or >10 mm in the short axis.
• Is able to provide an evaluable core or excisional lymph node biopsy for biomarker analysis from an archival or newly obtained biopsy at Screening (Visit 1).
• Has a performance status of 0 or 1 on the Eastern Cooperative Oncology Group (ECOG) Performance Scale.
• Has adequate organ function
• Female participants of childbearing potential must be willing to use an adequate method of contraception for the course of the study through 180 days after the last dose of study drug.
• Male participant of childbearing potential must be willing to use an adequate method of contraception starting with the first dose of study drug through 180 days after the last dose of study drug.

Exclusion Criteria:

• Has received previous treatment with brentuximab vedotin.
• Is currently participating in a study of an investigational agent and is currently receiving study therapy or has participated in a study of an investigational agent and has received study therapy or used an investigational device within 4 weeks of the first dose of study drug.
• Has a diagnosis of immunosuppression or is receiving systemic steroid therapy or any other form of immunosuppressive therapy within 7 days prior to the first dose of study drug.
• Has had a prior monoclonal antibody (mAb) within 4 weeks prior to first dose of study drug in the study or who has not recovered (i.e., ≤ Grade 1 or at baseline) from adverse events (AEs) due to agents administered more than 4 weeks earlier.
• Has had prior chemotherapy, targeted small molecule therapy, or radiation therapy within 2 weeks prior to study Day 1 or who has not recovered (i.e., ≤ Grade 1 or at baseline) from AEs due to a previously administered agent. Note: If a participant received major surgery, he/she must have recovered adequately from the toxicity and/or complications from the intervention prior to starting study drug.
• Has undergone prior allogeneic hematopoietic stem cell transplantation within the last 5 years. Note: Participants who have had a transplant greater than 5 years ago are eligible as long as there are no symptoms of graft-versus-host disease (GVHD).
• Has a known additional malignancy that is progressing or requires active treatment. Exceptions include basal cell carcinoma of the skin, squamous cell carcinoma of the skin, or in situ cervical cancer that has undergone potentially curative therapy.
• Has known active central nervous system (CNS) metastases and/or carcinomatous meningitis. Participants with previously treated brain metastases may participate provided they are stable (without evidence of progression by magnetic resonance imaging [MRI] for at least 4 weeks prior to the first dose of study drug and any neurologic symptoms have returned to baseline) and have no evidence of new or enlarging brain metastases.
• Has active autoimmune disease that has required systemic treatment in the past 2 years (i.e., with the use of disease modifying agents, corticosteroids, or immunosuppressive drugs).
• Has evidence of active, non-infectious pneumonitis.
• Has an active infection requiring intravenous systemic therapy.
• Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial.
• Is pregnant or breastfeeding, or expecting to conceive or father children within the projected duration of the trial, starting with the screening visit through 180 days after the last dose of study drug.
• Has received prior therapy with an anti-programmed cell death-1 (anti-PD-1), anti-PD-ligand 1 (anti-PD-L1), anti-PD-L2, anti-CD30, anti-CD137, or cytotoxic T-lymphocyte-associated protein 4 (CTLA-4) antibody (including ipilimumab) or any other antibody or drug specifically targeting T-cell co-stimulation or checkpoint pathways.
• Has a known history of human immunodeficiency virus (HIV)
• Has active hepatitis B (HBV) or hepatitis C (HCV).
• Has received a live vaccine within 30 days prior to first dose of study drug.