Inclusion Criteria:  STEP 0 (PRE-REGISTRATION) INCLUSION CRITERIA Patient must be >= 18 years of age on day of consent Patient must have an Eastern Cooperative Oncology Group (ECOG) performance status of 0-2  Patient must have a diagnosis of pancreatic cancer and have successfully undergone a curative intent surgical resection and must have no evidence of recurrent disease as determined by the investigator  NOTE: This includes patients with adenocarcinoma, acinar carcinoma, squamous cell carcinoma adenosquamous and variants thereof. Patients with neuroendocrine tumors are excluded from enrolling Patient must (1) be planning to receive, (2) be receiving or (3) have received at least three combined months (i.e., 12 weeks) of perioperative (neoadjuvant, adjuvant or a combination of both) systemic, multi-agent chemotherapy. Patients may have had up to 6 months of perioperative systemic therapy as deemed appropriate by their primary treating medical team (patients can have received radiation or chemoradiation in addition to this 6 month course) Patient must be no more than 12 weeks from their most recent treatment (this may be chemotherapy, radiotherapy or surgery) Patient must have a known pathogenic or likely pathogenic germline or somatic mutation in BRCA1, BRCA2, or PALB2, as determined by a Clinical Laboratory Improvement Amendments (CLIA) certified or equivalently-accredited laboratory. Mutations must be considered pathogenic or likely pathogenic by a reference database such as ClinVar or OncoKb.org STEP 1 (RANDOMIZATION) INCLUSION CRITERIA Patient must have met the eligibility criteria outlined above Patient must have undergone at least 3 combined months (i.e., 12 weeks) of perioperative (neoadjuvant, adjuvant or a combination of both) systemic, multi-agent chemotherapy. Patients may have had up to 6 months of perioperative systemic therapy as deemed appropriate by their primary treating medical team (patients can have received radiation or chemoradiation in addition to this 6 months course) Central expert reviewer must have determined the patient eligible for randomization after review of local genetic testing reports If mutation in BRCA1, BRCA2 or PALB2 was identified in tumor tissue and the patient has not previously undergone germline testing, the patient must agree to undergo germline testing Patient must not have previously had evidence of progressive pancreatic cancer while receiving platinum-based therapy Patient must be >= 21 days (three weeks) from their last treatment (including chemotherapy radiotherapy or surgery) but =< 84 days (twelve weeks) from their last treatment at the time of Step 1 randomization. Patients who have received neoadjuvant and/or adjuvant radiotherapy are eligible Patient must have recovered from any adverse events due to prior anti-cancer therapy (i.e., have no residual toxicities > grade 1 with the exception of alopecia and/or neuropathy) Leukocytes >= 3,000/mcL (obtained =< 14 days prior to Step 1 randomization) Absolute neutrophil count >= 1,500/mcL (obtained =< 14 days prior to Step 1 randomization) Platelets >= 100,000/mcL (obtained =< 14 days prior to Step 1 randomization) Hemoglobin >= 9.0 g/dL with no blood transfusion in the past 28 days (obtained =< 14 days prior to Step 1 randomization) Total bilirubin =< institutional upper limit of normal (ULN) except in patients with Gilbert's syndrome. Patients with Gilbert's syndrome may enroll if direct bilirubin =< 2.5 ULN of the direct bilirubin (obtained =< 14 days prior to Step 1 randomization) Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase [SGOT])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase [SGPT]) =< 2.5 institutional ULN (obtained =< 14 days prior to Step 1 randomization) Creatinine =< institutional ULN OR calculated Cockcroft Gault creatinine clearance > 50 mL/min/1.73 m^2 unless data exists supporting safe use at lower kidney function values, no lower than 30 mL/min/1.73 m^2 (obtained =< 14 days prior to Step 1 randomization) Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated 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, they are eligible if they have an undetectable HCV viral load Patient must have the ability to understand the willingness to sign a written informed consent document, or have legally authorized representative provide authorization to participate  Exclusion Criteria:  STEP 1 (RANDOMIZATION) EXCLUSION CRITERIA Patient must have no evidence of recurrent or metastatic pancreatic cancer at the time of randomization as documented by baseline scans obtained =< 4 weeks prior to Step 1 randomization Patient must not be receiving any other investigational agents at the time of Step 1 randomization and while on protocol treatment Patient must not have any history of allergic reactions attributed to compounds of similar chemical or biological composition to olaparib Patient must not have any personal history of myelodysplastic syndrome (MDS) or acute myeloid leukemia (AML). Patients with myelodysplastic syndrome/acute myeloid leukemia or with features suggestive of MDS/AML. Patient must not have any uncontrolled gastrointestinal disorder that would, in the opinion of the investigator, interfere with the ingestion or absorption of olaparib Patient must not be pregnant or breast-feeding due the potential harm to an unborn fetus and possible risk for adverse events in nursing infants with the treatment regimens being used. All patients of childbearing potential must have a blood test or urine study within 14 days prior to Step 1 randomization to rule out pregnancy. A patient of childbearing potential is defined as anyone, regardless of sexual orientation or whether they have undergone tubal ligation, who meets the following criteria: 1) has achieved menarche at some point, 2) has not undergone a hysterectomy or bilateral oophorectomy; or 3) has not been naturally postmenopausal (amenorrhea following cancer therapy does not rule out childbearing potential) for at least 24 consecutive months (i.e., has had menses at any time in the preceding 24 consecutive months) Patients must not expect to conceive or father children by using accepted and effective method(s) of contraception or by abstaining from sexual intercourse for the duration of their participation in the study and for 6 months after the last dose of protocol treatment for female patients and for 3 months after the last dose of protocol treatment for male patients. Patients must also not donate sperm while on protocol treatment and for 3 months after the last dose of protocol treatment. Patients must also not breast-feed while on protocol treatment and for 1 month after the last dose of protocol treatment Patient must not have resting electrocardiogram (ECG) indicating uncontrolled, potentially reversible cardiac conditions, as judged by the investigator (e.g. unstable ischemia, uncontrolled symptomatic arrhythmia, congestive heart failure, corrected QT (QTc) prolongation > 500 ms, electrolyte disturbances, etc.) or have congenital long QT syndrome Concomitant use of known potent CYP3A4/5 inhibitors such as ketoconazole, itraconazole, ritonavir, indinavir, saquinavir, telithromycin, clarithromycin and nelfinavir is prohibited Patients who are being actively treated for an ongoing concurrent malignancy are ineligible, with the exception of those receiving adjuvant hormone therapies and those receiving topical therapies for skin cancers Patient must not have, in the opinion of the investigator, any other concurrent medical condition that would prevent the patient from complying with the study procedures Patient must not be considered a poor medical risk due to a serious, uncontrolled medical disorder, non-malignant systemic disease or active, uncontrolled infection. Examples include, but are not limited to, uncontrolled ventricular arrhythmia, recent (within 3 months) myocardial infarction, uncontrolled major seizure disorder, unstable spinal cord compression, superior vena cava syndrome, extensive interstitial bilateral lung disease on high resolution computed tomography (HRCT) scan or any psychiatric disorder that prohibits obtaining informed consent Patient must not have had major surgery within 2 weeks prior to randomization and patients must have recovered from any effects of any major surgery