Inclusion Criteria:

          -  Have signed an informed consent document

          -  Be willing/able to adhere to the prohibitions and restrictions specified in this
             protocol

          -  Written authorization for use and release of health and research study information has
             been obtained

          -  Life expectancy >= 10 years (as determined by the treating physician)

          -  Eastern Cooperative Oncology Group (ECOG) performance status =< 1

          -  Histologically confirmed adenocarcinoma of the prostate as documented by a minimum 12
             core prostate biopsy completed within 1-year of enrollment (note: most recent prostate
             biopsy must have demonstrated prostatic adenocarcinoma)

          -  Favorable risk prostate cancer as defined by:

               -  Very low-risk:

                    -  Clinical stage T1c disease

                    -  PSA density (PSAD) < 0.15 ng/mL

                    -  Gleason score 6

                    -  =< 2 core biopsies with =< 50% involvement of any biopsy core with cancer,
                       or unilateral disease =< 2 core biopsies with any percentage involvement OR

               -  Low risk:

                    -  Clinical stage =< T2a

                    -  PSA < 15 ng/mL

                    -  Gleason score 6 OR

               -  Low-intermediate risk:

                    -  Clinical stage T1c

                    -  PSA < 15 ng/ml

                    -  Gleason 3+4 present in =< 50% of one core/site as detected by systematic
                       biopsy or MRI/transrectal ultrasound (TRUS) fusion guided biopsy

                    -  Gleason 6 disease in all other cores / sites

          -  Willing and qualified for active surveillance at Johns Hopkins or the University of
             Washington

          -  Serum testosterone >= 150 ng/dL

          -  Able to swallow the study drugs whole as a tablet

          -  Hemoglobin >= 9.0 g/dL, (at screening), independent of transfusion and/or growth
             factors within 3 months prior to registration

          -  Platelet count >= 100,000 x 10^9/uL (at screening) independent of transfusion and/or
             growth factors within 3 months prior to registration

          -  Serum albumin >= 3.0 g/dL (at screening)

          -  Glomerular filtration rate (GFR) >= 45 mL/min (at screening)

          -  Serum potassium >= 3.5 mmol/L (at screening)

          -  Serum total bilirubin =< 1.5 x upper limit of normal (ULN) (at screening) (note: in
             subjects with Gilbert's 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)

          -  Aspartate aminotransferase (AST) or alanine aminotransferase (ALT) < 2.5 × ULN (at
             screening)

          -  Medications known to lower the seizure threshold must be discontinued or substituted
             at least 4 weeks prior to study entry

          -  Agrees to use a condom (even men with vasectomies) and another effective method of
             birth control if he is having sex with a woman of childbearing potential or agrees to
             use a condom if he is having sex with a woman who is pregnant while on study drug and
             for 3 months following the last dose of study drug; must also agree not to donate
             sperm during the study and for 3 months after receiving the last dose of study drug

        Exclusion Criteria:

          -  Prior local therapy to treat prostate cancer (e.g. radical prostatectomy, radiation
             therapy, brachytherapy)

          -  Prior use of ARN-509 (apalutamide)

          -  Have known allergies, hypersensitivity, or intolerance to ARN-509 (apalutamide) or its
             excipients

          -  Prior or ongoing systemic therapy for prostate cancer including, but not limited to:

               -  Hormonal therapy (e.g. leuprolide, goserelin, triptorelin)

               -  Cytochrome P450 (CYP)-17 inhibitors (e.g. abiraterone, ketoconazole)

               -  Antiandrogens (e.g. bicalutamide, nilutamide)

               -  Second generation antiandrogens (e.g. enzalutamide)

               -  Immunotherapy (e.g. sipuleucel-T, ipilimumab)

               -  Chemotherapy (e.g. docetaxel, cabazitaxel)

          -  Have any condition that, in the opinion of the investigator, would compromise the
             well-being of the subject or the study or prevent the subject from meeting or
             performing study requirements

          -  History of any of the following:

               -  Seizure or known condition that may pre-dispose to seizure (including but not
                  limited to prior stroke, transient ischemic attack, loss of consciousness within
                  1 year prior to registration, brain arteriovenous malformation; or intracranial
                  masses such as schwannomas and meningiomas that are causing edema or mass effect)

               -  Severe or unstable angina, myocardial infarction, symptomatic congestive heart
                  failure, arterial or venous thromboembolic events (e.g., pulmonary embolism,
                  cerebrovascular accident including transient ischemic attacks), or clinically
                  significant ventricular arrhythmias within 6 months prior to registration

               -  Any condition that in the opinion of the investigator, would preclude
                  participation in this study

          -  Current evidence of any of the following:

               -  Uncontrolled hypertension

               -  Gastrointestinal disorder affecting absorption

               -  Active infection (e.g. human immunodeficiency virus [HIV] or viral hepatitis) or
                  other medical condition that would make prednisone/prednisolone (corticosteroid)
                  use contraindicated

               -  Any condition that in the opinion of the investigator, would preclude
                  participation in this study

          -  The use of drugs known to lower the seizure threshold, including: atypical
             antipsychotics (e.g. clozapine, olanzapine, risperidone, ziprasidone), bupropion,
             lithium, meperidine, pethidine, phenothiazine antipsychotics (e.g. chlorpromazine,
             mesoridazine, thioridazine), and tricyclic antidepressants (e.g. amitriptyline,
             desipramine, doxepin, imipramine, maprotiline, mirtazapine)

          -  The use of strong CYP3A4 inhibitors, including: itraconazole, clarithromycin,
             erythromycin, diltiazem, verapamil, delavirdine, atazanavir, indinavir, nefazodone,
             nelfinavir, ritonavir, saquinavir, telithromycin, voriconazole, grapefruit juice (or
             grapefruits)

               -  Note: If a patient is on a strong CYP3A4 inhibitor, they can be reconsidered for
                  enrollment if they can safely stop said medication; a two week or 5 half-lives,
                  whichever is longer, washout will be required prior to enrolling on study;
                  subject may not resume medication while receiving apalutamide

          -  Strong CYP3A4 inducers, including: phenytoin, carbamazepine, rifampin, rifabutin,
             rifapentine, phenobarbital, efavirenz, tipranavir, St. John's wort

             **Note: If a patient is on a strong CYP3A4 inhibitor, they can be reconsidered for
             enrollment if they can safely stop said medication; a two week or 5 half-lives,
             whichever is longer, washout will be required prior to enrolling on study; subject may
             not resume medication while receiving apalutamide

          -  Any psychological, familial, sociological, or geographical condition that could
             potentially interfere with compliance with the study protocol and follow-up schedule