Inclusion Criteria:

          -  Histologically confirmed (within 180 days prior to registration) adenocarcinoma of the
             prostate at high risk for recurrence as determined by the following criteria,
             according to American Joint Committee on Cancer (AJCC) 8th edition:

               -  Phase I enrollment

                    -  Gleason >= 9, PSA =< 150 ng/mL, any T-stage

               -  Phase II enrollment

                    -  Gleason >= 9, PSA =< 150 ng/mL, any T-stage

                    -  Gleason 8, PSA < 20 ng/mL, and >= T2

                    -  Gleason 8, PSA >= 20-150 ng/mL, any T-stage

                    -  Gleason 7, PSA >= 20-150 ng/mL, any T-stage

          -  No distant metastases as evaluated by:

               -  Bone scan 90 days prior to registration

               -  Lymph node assessment by computed tomography (CT) or magnetic resonance (MR) of
                  pelvis or nodal sampling within 90 days prior to registration (Please note: Lymph
                  nodes will be considered negative (N0) if they are < 1.5 cm short axis)

          -  History/physical examination within 90 days prior to registration

          -  Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 within 180 days
             prior to registration

          -  Pretreatment serum PSA, obtained prior to any androgen suppression therapy and within
             180 days of registration

          -  Phase I patients: Prior androgen suppression for prostate cancer is not allowed prior
             to registration

          -  Phase II patients: Prior androgen suppression for prostate cancer is allowed =< 45
             days prior to registration

          -  Hemoglobin >= 9.0 g/dL (within 90 days prior to registration)

          -  Platelets >= 100,000 cells/mm^3 (within 90 days prior to registration)

          -  Absolute neutrophil count (ANC) >= 1.5 x 10^9/L (within 90 days prior to registration)

          -  Serum creatinine =<1.5 x upper limit of normal (ULN) OR a calculated creatinine
             clearance >= 30 mL/min estimated using Cockcroft-Gault equation (within 90 days prior
             to registration)

          -  Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =< 3.0 x ULN
             (within 90 days prior to registration)

          -  Serum albumin >= 3 g/dL (within 90 days prior to registration)

          -  Serum potassium >= 3.5 mg/dL (within 90 days prior to registration)

          -  Serum total bilirubin =< 1.5 x ULN or direct bilirubin =< 1 x ULN (Note: in subjects
             with Gilberts syndrome, if total bilirubin is > 1.5 x ULN, measure direct and indirect
             bilirubin, and if direct bilirubin is =< 1.5 x ULN, subject may be eligible) (within
             90 days prior to registration)

          -  Men of child-producing potential must be willing to consent to use effective
             contraception while on treatment and for at least 3 months afterwards

          -  The patient or a legally authorized representative must provide study-specific
             informed consent prior to study entry

        Exclusion Criteria:

          -  PSA > 150 ng/mL

          -  Definitive clinical or radiologic evidence of metastatic disease

          -  Pathologically positive lymph nodes or nodes > 1.5 cm short axis on CT or MR imaging

          -  Prior radical prostatectomy, cryosurgery for prostate cancer, or bilateral orchiectomy
             for any reason

          -  Any active malignancy within 2 years of study registration that may alter the course
             of prostate cancer treatment.

          -  Prior systemic therapy for prostate cancer; note that prior therapy for a different
             cancer is allowable

          -  Prior radiotherapy, including brachytherapy, to the region of the prostate that would
             result in overlap of radiation therapy fields

          -  Current treatment with first generation anti-androgens (bicalutamide, nilutamide,
             flutamide). For patients enrolled to phase II, if prior anti-androgens were
             administered, a washout period of >= 30 days is required prior to enrollment

          -  Severe, active co-morbidity, defined as follows:

               -  Unstable angina and/or congestive heart failure requiring hospitalization within
                  the last 6 months

               -  Transmural myocardial infarction within the last 6 months

               -  Acute bacterial or fungal infection requiring intravenous antibiotics at the time
                  of registration

               -  Uncontrolled acquired immune deficiency syndrome (AIDS) based upon current
                  Centers for Disease Control and Prevention (CDC) definition

               -  Presence of uncontrolled hypertension (persistent systolic blood pressure [BP]
                  >=160 mmHg or diastolic BP >= 100 mmHg). Subjects with a history of hypertension
                  are allowed, provided that BP is controlled to within these limits by
                  anti-hypertensive treatment

          -  Prior allergic reaction to the drugs involved in this protocol (including known
             allergies, hypersensitivity or intolerance to the excipients of niraparib. Please see
             Niraparib IB for details.)

          -  Human immunodeficiency virus (HIV) positive with CD4 count < 200 cells/microliter

               -  Note that patients who are HIV positive are eligible, provided they have a CD4
                  count >= 200 cells/microliter within 90 days prior to registration. Patients
                  receiving treatment with highly active antiretroviral therapy (HAART) will not be
                  eligible due to concern for radiosensitization

               -  Note also that HIV testing is not required for eligibility for this protocol.
                  This exclusion criterion is necessary because the treatments involved in this
                  protocol may be affected by these drugs.

          -  Any history or current diagnosis of Myelodysplasitc Syndromes (MDS)/ Acute Myeloid
             Leukemia (AML).

          -  Prior or current treatment with PARP inhibitor