Inclusion Criteria:

          1. Histologically confirmed diagnosis of high-grade glioma (HGG) in any tumor sample and
             presence of histone H3 K27M mutation detected in a Clinical Laboratory Improvement
             Amendment (CLIA) certified laboratory by immunohistochemistry or DNA sequencing test
             on any glioma tumor sample.

          2. Unequivocal evidence of progressive disease on contrast-enhanced brain CT or MRI as
             defined by RANO-HGG criteria, or have documented recurrent glioma on diagnostic
             biopsy.

          3. Measurable disease by RANO-HGG criteria.

          4. Patients must have had previous therapy with at least radiotherapy.

          5. No more than two prior episodes of recurrence from radiotherapy and/or chemotherapy.
             Use of bevacizumab solely for treatment of radiation necrosis, pseudoprogression, or
             treatment effect will not be considered a recurrence.

          6. Interval of at least 90 days from the completion of radiotherapy to the first dose of
             ONC201. If patients are within 90 days of radiotherapy, they may still be eligible if
             they meet one or more of the following criteria.

               1. Progressive tumor is outside the original high-dose radiotherapy target volume as
                  determined by the treating investigator, or

               2. Histologic confirmation of tumor through biopsy or resection, or

               3. Nuclear medicine imaging, MR spectroscopy, or MR perfusion imaging consistent
                  with true progressive disease, rather than pseudoprogression or radiation
                  necrosis obtained within 28 days of registration.

          7. From the projected start of scheduled study treatment, the following time periods must
             have elapsed: 5 half-lives from any investigational agent, 4 weeks from cytotoxic
             therapy (except 23 days for temozolomide and 6 weeks from nitrosoureas), 6 weeks from
             antibodies, or 4 weeks (or 5 half-lives, whichever is shorter) from other anti-tumor
             therapies.

          8. All adverse events Grade > 1 related to prior therapies (chemotherapy, radiotherapy,
             and/or surgery) must be resolved to grade 1 or baseline, except for alopecia and
             sensory neuropathy Grade ≤ 2, or other Grade ≤ 2 not constituting a safety risk based
             on investigator's judgment, are acceptable.

          9. Male or Female age ≥18 years.

         10. Karnofsky Performance Status (KPS) ≥ 60 (see Appendix A).

         11. Adequate organ and marrow function as defined below, all screening labs should be
             performed within 14 days of treatment initiation:

               -  leukocytes ≥ 3,000/mcL

               -  absolute neutrophil count ≥ 1,500/mcL

               -  platelets ≥ 75,000/mcL

               -  hemoglobin > 8.0 mg/dL

               -  total bilirubin ≤ 2.0 x upper limit of normal

               -  AST (SGOT)/ALT (SGPT) ≤ 2.5 × upper limit of normal

               -  creatinine ≤ ULN OR creatinine clearance ≥60 mL/min/1.73 m2 for patients with
                  creatinine levels above normal.

         12. Contrast-enhanced head CT or brain MRI and entire spine MRI within 14 days prior to
             start of study drug.

         13. Corticosteroid dose must be stable or decreasing for at least 3 days prior to the
             baseline CT or MRI scan.

         14. The effects of ONC201 on the developing human fetus are unknown. For this reason,
             women of childbearing potential (WOCBP) and men must agree to use adequate
             contraception prior to study entry and for the duration of study participation and for
             30 days after the last dose of therapy. Highly effective contraceptive measures
             include: stable use of oral contraceptives such as combined estrogen and progestogen
             and progestogen only hormonal contraception or other prescription pharmaceutical
             contraceptives for 2 or more menstrual cycles prior to screening; intrauterine device
             [IUD]; intrauterine hormone- releasing system (IUS); bilateral tubal ligation;
             vasectomy and sexual abstinence.

               1. WOCBP must have a negative serum or urine pregnancy test within 28 days of
                  initiation of dosing.

               2. Contraception is not required for men with documented vasectomy.

               3. Postmenopausal women must be amenorrheic for at least 12 months in order not to
                  be considered of childbearing potential.

               4. Pregnancy testing and contraception are not required for women with documented
                  hysterectomy or tubal ligation.

         15. Availability of a paraffin-embedded or frozen tumor-tissue block with a minimum of 1
             cm2 of tumor surface area, or 20 unstained slides from the tumor tissue specimen if a
             tumor block cannot be submitted. If a patient has had only a stereotactic biopsy, then
             5 unstained slides may be accepted with prior approval from the Sponsor, however all
             efforts must be made to obtain as close to 20 slides as possible.

         16. Ability to be able to swallow and retain orally administered medication

         17. Ability to understand and the willingness to sign a written informed consent document.
             Only subjects who have capacity to consent will be enrolled in the study.

        Exclusion Criteria:

          1. Arm B: Primary malignant lesion located in the pons or spinal cord.

          2. Arm B: Atypical non-astrocytic histologies such as ependymoma, ganglioma and
             pleomorphic xanthoastrocytoma, or pilocytic astrocytoma and subependymal giant cell
             astrocytoma (SEGA).

          3. Arm B: Prior bevacizumab treatment of >4 doses of >7.5 mg/Kg

          4. History of allergic reactions attributed to compounds of similar chemical or biologic
             composition to ONC201 or its excipients (See Section 8).

          5. Current or planned participation in a study of an investigational agent or using an
             investigational device.

          6. Presence of diffuse leptomeningeal disease or evidence of CSF dissemination.

          7. Uncontrolled intercurrent illness including, but not limited to, ongoing or active
             infection or psychiatric illness/social situations that would limit compliance with
             study requirements.

          8. Active infection requiring systemic therapy.

          9. Pregnant and/or breastfeeding women or unable to maintain use of contraception while
             on study and for 30 days after the last dose of study drug. ONC201 is a novel agent
             with unknown potential for teratogenic or abortifacient effects. Because there is an
             unknown but potential risk for adverse events in nursing infants, secondary to
             treatment of the mother with ONC201, breastfeeding should be discontinued if the
             mother is treated with ONC201.

         10. Known HIV-positive test on combination antiretroviral therapy.

         11. Known history of cardiac arrhythmias including atrial fibrillation, tachyarrhythmias
             or bradycardia, unless arrhythmia is controlled and after Cardiology has cleared
             patient to receive ONC 201. Receiving therapeutic agents known to prolong QT interval
             will be excluded. History of CHF, or MI or stroke in the last 3 months will be
             excluded.

         12. Active illicit drug use or diagnosis of alcoholism.

         13. Tumors with known IDH1 (isocitrate dehydrogenase 1) or known IDH2 mutations as
             determined by immunohistochemistry for the IDH1 R132H variant or by direct sequencing.
             IDH1/2-mutant gliomas have a markedly longer overall survival rate compared to those
             with IDH1/2-wildtype glioma (Parsons et al., 2008; Yan et al., 2009), indicating
             IDH1/2-mutant gliomas have a distinct natural history.

         14. Tumors with known 1p/19q co-deletion.

         15. Known additional malignancy that is progressing or requires active treatment within 3
             years of start of study drug. Exceptions include basal cell carcinoma of the skin,
             squamous cell carcinoma of the skin, in situ melanoma, or in situ cervical cancer that
             has undergone potentially curative therapy.

         16. Any surgery (not including minor diagnostic procedures such as lymph node biopsy)
             within 2 weeks of baseline disease assessments; or not fully recovered from any side
             effects of previous procedures. An interval of 1 week for stereotactic brain biopsy
             from the start of study treatment is acceptable.

         17. Concomitant use of potent CYP3A4/5 inhibitors during the treatment phase of the study
             and within 72 hours prior to starting study drug administration.

         18. Concomitant use of potent CYP3A4/5 inducers, which include enzyme inducing
             antiepileptic drugs (EIAEDs) (see Appendix B), during the treatment phase of the study
             and within 2 weeks prior to starting treatment. Concurrent dexamethasone is allowed.