Inclusion Criteria:

   - Patients must have tissue confirmation of high grade (WHO Grade IV) glioma including
   but not limited to glioblastoma, gliosarcoma, glioblastoma with oligodendroglial
   features, glioblastoma with PNET features.

   - The patient must have post-operative contrast enhanced imaging (CT or MRI) unless only
   biopsy performed (in which case post-operative imaging is not routinely obtained. In
   these patients, the preoperative study will serve as baseline.

   - Patient should have surgery (biopsy, partial resection or gross total resection) and
   no additional anti-cancer therapy except the chemoradiation as specified in the
   protocol.

   - For those patients in which steroids are clinically indicated, there must be a stable
   or decreasing dose of steroid medication for ≥ one week prior to the start of
   infusion.

   - Patients must be between the ages of 18 and 75 years old.

   - Patients must have Karnofsky Performance score ≥ 60.

   - Adequate organ function is needed at time of screening visit including:

      - ANC ≥ 1500

      - Platelets ≥ 100,000 ml

      - Serum Creatinine ≤ 1.5mg/dl; Cr Clearance should be >50 mL/min

      - AST and ALT ≤ 3 times the upper limit of normal

      - If female of childbearing potential, negative pregnancy test

   - The patient or his/her legal representative must have the ability to understand and
   willingness to sign a written informed consent document.

   - Patient agrees to use an effective method of contraception (hormonal or two barrier
   methods) while on study and for at least 3 months following the Plerixafor infusion

Exclusion Criteria:

   - Prior or concurrent treatment with Avastin (bevacizumab)

   - Prior exposure to Plerixafor

   - Prior use of other investigational agents to treat the brain tumor

   - Recent history of myocardial infarct (less than 3 months) or history of active angina
   or arrhythmia

   - Prior malignancy except previously diagnosed and definitively treated more than 3
   years prior to trial or whose prognosis is deemed good enough to not warrant
   surveillance

   - Prior sensitivity to Plerixafor

   - Pregnant or patients who are breastfeeding