Inclusion Criteria:

          -  Patient must have a histologic or cytologic diagnosis of pancreatic adenocarcinoma.
             Patients with neuroendocrine tumors, acinar cell and adenosquamous carcinomas are
             excluded. All disease must be assessed and documented on the Baseline Tumor Assessment
             Form

          -  Patients must have one of the following mutations: germline mutation in BRCA 1 or 2
             that was tested in a Clinical Laboratory Improvement Act (CLIA) certified lab defined
             as positive and/or deleterious (that is, pathogenic or likely pathogenic variant).
             (NOTE: Patients with tumor somatic mutations are not eligible)

          -  Patient must have metastatic disease and received first line platinum-based
             chemotherapy (i.e. fluorouracil, irinotecan, leucovorin and oxaliplatin [FOLFIRINOX],
             leucovorin calcium, 5-fluorouracil, and oxaliplatin [FOLFOX], or gemcitabine +
             cisplatin)

          -  Patients must have had a computed tomography (CT) or magnetic resonance imaging (MRI)
             showing stable or responding disease on first line platinum-based chemotherapy within
             30 days prior to registration

          -  Patients with known human immunodeficiency virus (HIV)-infection are eligible
             providing they are on effective anti-retroviral therapy and have undetectable viral
             load at their most recent viral load test and within 6 months prior to registration

          -  Patients with history of chronic hepatitis B virus (HBV) infection must have
             undetectable HBV viral load within 30 days prior to registration

          -  Patients with a history of hepatitis C virus (HCV) infection must have been treated
             and cured. For patients with HCV infection who are currently on treatment must have an
             undetectable HCV viral load within 30 days prior to registration

          -  Patients must have received at least 16 weeks but no more than 24 weeks of first line
             platinum-based therapy for metastatic disease

          -  Patients' last chemotherapy treatment must be within 30 days prior to registration

          -  Patients must have resolved or stable =< grade 1 toxicity from prior administration of
             another investigational drug and/or prior anti-cancer treatment, excluding neuropathy
             and alopecia

          -  Zubrod performance status of 0-1

          -  Patients must have a complete medical history and physical exam within 28 days prior
             to registration

          -  Absolute neutrophil count >= 1,500/mcL (within 14 days of registration)

          -  Platelets >= 100,000/mcL (within 14 days of registration)

          -  Total bilirubin =< 1.5 institutional upper limit of normal (ULN) (within 14 days of
             registration)

          -  Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) =< 3 x institutional
             ULN (within 14 days of registration)

          -  Creatinine =< 1.5 mg/dl (within 14 days of registration)

          -  Albumin >= 3.0 (within 14 days of registration)

          -  Hemoglobin >= 9.0 g/dL

          -  Patients must have CA19-9 obtained within 42 days prior to registration

          -  Patients must be able to swallow and retain oral medications and have no known
             gastrointestinal disorders likely to interfere with absorption of the study medication

          -  Participants with a prior or concurrent malignancy whose natural history or treatment
             (in the opinion of the treating physician) does not have the potential to interfere
             with the safety or efficacy assessment of the investigational regimen are eligible for
             this trial provided it does not require concurrent therapy

          -  Patients must be offered the opportunity to participate in specimen banking of
             formalin-fixed paraffin-embedded (FFPE) tissue and whole blood. If a patient is unable
             to submit archival tissue, should the patient need to undergo a standard of care
             biopsy per National Comprehensive Cancer Network (NCCN) guidelines, patients must then
             be offered the opportunity to submit the fresh tumor tissue from that biopsy. With
             participant consent, specimens must be collected and submitted via the Southwest
             Oncology Group (SWOG) Specimen Tracking System

          -  Patients must be informed of the investigational nature of this study and must sign
             and give informed consent in accordance with institutional and federal guidelines. For
             participants with impaired decision making capabilities, legally authorized
             representatives may sign and give informed consent on behalf of study participants in
             accordance with applicable federal, local, and Canada Industrial Relations Board
             (CIRB) regulations

          -  As a part of the Oncology Patient Enrollment Network (OPEN) registration process the
             treating institution's identity is provided in order to ensure that the current
             (within 365 days) date of institutional review board approval for this study has been
             entered in the system

        Exclusion Criteria:

          -  Patients must not have a known hypersensitivity to olaparib or any of the excipients
             of the product

          -  Patients must not be planning to receive strong or moderate CYP3A inhibitors or
             inducers while on olaparib treatment. Patients receiving strong or moderate CYP3A
             inhibitors must discontinue use at least 2 weeks prior to receiving olaparib. Patients
             receiving strong or moderate CYP3A inducers must discontinue use at least 5 weeks
             prior to receiving olaparib. Medications should be checked using a frequently updated
             medical reference for a list of drugs to avoid

          -  Patients must not have received live vaccines within 42 days prior to randomization
             and must not be planning to receive live virus or live bacterial vaccines while
             receiving study treatment and during the 30 day follow up period. Examples of live
             vaccines include, but are not limited to, the following: measles, mumps, rubella,
             chicken pox, shingles, yellow fever, rabies, Bacillus Calmette-Guerin (BCG), and
             typhoid (oral) vaccine. Seasonal influenza vaccines for injection are generally killed
             virus vaccines and are allowed; however, intranasal influenza vaccines (e.g.,
             Flu-Mist) are live attenuated vaccines, and are not allowed

          -  Patients must not have had prior therapy with an anti-PD-1, anti-PD-L1, or anti-PD-L2
             agent, or any other immune checkpoint inhibitors

          -  Patients must not have had prior therapy with PARP inhibitors

          -  Patients must not have had a prior diagnosis of immunodeficiency or receiving systemic
             steroid therapy (defined as >= 10 mg prednisone or equivalent) or any other form of
             immunosuppressive therapy within 7 days prior to the first dose of trial treatment

          -  Participants must not be pregnant or nursing due to the possibility of harm to the
             fetus or nursing infant from this treatment regimen. Women/men of reproductive
             potential must have agreed to use an effective contraceptive method for the course of
             the study through 6 months after the last dose of study medication. A woman is
             considered to be of "reproductive potential" if she has had menses at any time in the
             preceding 12 consecutive months. In addition to routine contraceptive methods,
             "effective contraception" also includes heterosexual celibacy and surgery intended to
             prevent pregnancy (or with a side-effect of pregnancy prevention) defined as a
             hysterectomy, bilateral oophorectomy or bilateral tubal ligation. However, if at any
             point a previously celibate participant chooses to become heterosexually active during
             the time period for use of contraceptive measures, he/she is responsible for beginning
             contraceptive measures. Should a woman become pregnant or suspect she is pregnant
             while she or her partner is participating in this study, she should inform her
             treating physician immediately

          -  Patients must not have a history of (non-infectious) pneumonitis that required
             steroids or current pneumonitis

          -  Patients must not have an active infection requiring systemic therapy

          -  Patients must not have active autoimmune disease that has required systemic treatment
             in 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