Inclusion Criteria:

          -  Have a diagnosis of ovarian, fallopian tube, or primary peritoneal cancer who have
             received systemic chemotherapy including platinum-based chemotherapy

          -  Have a cancer antigen (CA)-125 that normalized after first-line therapy

          -  CA-125 increased to more than twice the upper limit of normal or two times the nadir
             value after most recent second or later line of treatment

          -  Have no measurable disease based on Response Evaluation Criteria in Solid Tumors
             (RECIST) 1.1. Ascites and pleural effusions are not measurable disease, if
             asymptomatic

          -  All patients who are having sex that can lead to pregnancy must agree to contraception
             for the duration of the study

          -  Have estimated life expectancy of at least 3 months

          -  Be willing and able to provide written informed consent/assent for the trial

          -  Have a performance status of 0 or 1 on the on the Eastern Cooperative Oncology Group
             (ECOG) performance scale

          -  Absolute neutrophil count (ANC) >= 1,500/mcL (performed within 10 days of treatment
             initiation)

          -  Platelets >= 100,000/mcL (performed within 10 days of treatment initiation)

          -  Hemoglobin (Hgb) >= 9 g/dL or >= 5.6 mmol/L without transfusion or erythropoietin
             (EPO) dependency (within 7 days of assessment)

          -  Creatinine =< 1.5 x upper limit of normal (ULN) OR measured or calculated creatinine
             clearance >= 30 mL/min for subject with creatinine levels > 1.5 x institutional ULN

          -  Serum total bilirubin =< 1.5 X ULN OR direct bilirubin =< ULN for subjects with total
             bilirubin levels > 1.5 X ULN (performed within 10 days of treatment initiation)

          -  Aspartate transaminase (AST) (serum glutamic-oxaloacetic transaminase [SGOT]) and
             alanine transferase (ALT) (serum glutamate pyruvate transaminase [SGPT]) =< 2.5 X ULN
             OR =< 5 X ULN for subjects with liver metastases (performed within 10 days of
             treatment initiation)

          -  International normalized ratio (INR) or prothrombin time (PT) =< 1.5 X ULN unless
             patient is receiving anticoagulant therapy (as long as PT or partial thromboplastin
             time [PTT] is within therapeutic range of intended use of anticoagulants) (performed
             within 10 days of treatment initiation)

          -  Activated partial thromboplastin time (aPTT) =< 1.5 X ULN unless patient is receiving
             anticoagulant therapy (as long as PT or PTT is within therapeutic range of intended
             use of anticoagulants) (performed within 10 days of treatment initiation)

        Exclusion Criteria:

          -  Is currently participating and receiving study therapy or has participated in a study
             of an investigational agent and received study therapy within 4 weeks of the first
             dose of treatment

          -  Has a diagnosis of immunodeficiency or is receiving systemic steroid therapy (if
             dosing exceeding 10 mg daily of prednisone equivalent) or any other form of
             immunosuppressive therapy within 7 days prior to the first dose of trial treatment

          -  Short-term administration of systemic steroids (i.e., for allergic reactions or the
             management of immune-related adverse events [irAEs]) is allowed

          -  Has symptomatic ascites or pleural effusions

          -  History of borderline or low malignant potential ovarian cancer

          -  Has a known history of active TB (Bacillus Tuberculosis)

          -  Hypersensitivity to pembrolizumab or any of its excipients

          -  Has had a prior anti-cancer monoclonal antibody (mAb) within 4 weeks prior to study
             day 1 or who has not recovered (i.e., =< grade 1 or at baseline) from adverse events
             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 adverse events due to a previously administered agent.

               -  Note: Patients with =< grade 2 neuropathy are an exception to this criterion and
                  may qualify for the study

               -  Note: If a patient received major surgery, they must have recovered adequately
                  from the toxicity and/or complications from the intervention prior to starting
                  therapy

          -  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

          -  Has known active central nervous system (CNS) metastases and/or carcinomatous
             meningitis. Patients with previously treated brain metastases may participate provided
             they are stable (without evidence of progression by imaging for at least four weeks
             prior to the first dose of trial treatment and any neurologic symptoms have returned
             to baseline), have no evidence of new or enlarging brain metastases, and are not using
             steroids for at least 14 days prior to trial treatment. This exception does not
             include carcinomatous meningitis which is excluded regardless of clinical stability

          -  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

          -  Has a history of (non-infectious) pneumonitis that required steroids or current
             pneumonitis

          -  Has an active infection requiring systemic therapy

          -  Has a history or current evidence of any condition, therapy, or laboratory abnormality
             that might confound the results of the trial, interfere with the patient's
             participation for the full duration of the trial, or is not in the best interest of
             the patient to participate, in the opinion of the treating investigator

          -  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 children within the projected
             duration of the trial, starting with the pre-screening or screening visit through 120
             days after the last dose of trial treatment

          -  Clinically significant cardiovascular disease

          -  Known severe hypersensitivity reactions to monoclonal antibodies or carboplatin >=
             grade 3, any history of anaphylaxis, or uncontrolled asthma

          -  Has received prior therapy with pembrolizumab

          -  Has a known history of human immunodeficiency virus (HIV) (HIV 1/2 antibodies)

          -  Has known active hepatitis B (e.g., hepatitis B surface antigen [HBsAg] reactive) or
             hepatitis C (e.g., hepatitis C virus [HCV] ribonucleic acid [RNA] [qualitative] is
             detected)

          -  Has received a live vaccine within 30 days of planned start of study therapy.

               -  Note: Seasonal influenza vaccines for injection are generally inactivated flu
                  vaccines and are allowed; however intranasal influenza vaccines (e.g., Flu-Mist)
                  are live attenuated vaccines, and are not allowed