Autologous T Cells Redirected to EGFRVIII-With a Chimeric Antigen Receptor in Patients With EGFRVIII+ Glioblastoma

Inclusion Criteria: * Pathological criteria: Glioblastoma (GBM) that is histologically confirmed by pathology review of surgically resected tissue. * Tumor cells from resected tissue must be available for EGFRvIII testing. Patients who have previously been treated with an EGFRvIII-targeted therapy and recurred, must have a tumor sample obtained after their recurrence available for EGFRvIII testing. * Age greater than 18 years. * If the patient is on dexamethasone, the anticipated dose must be 4 mg/day or less for at least 5 days prior to apheresis. * ECOG performance status of 0 or 1 Documented negative serum HCG for female patients of child-bearing potential. * Participants with adequate organ function as measured by: * White blood count greater than or equal to 2500/mm\^3; platelets greater than or equal to 100,000/mm\^3, hemoglobin greater than or equal to 9.0 g/dL; without transfusion or growth factor support * AST, ALT, GGT, LDH, alkaline phosphatase within 2.5 x upper normal limit, and total bilirubin less than or equal to 2.0 mg/dL * Serum creatinine less than or equal to 1.5 x upper limit of normal * Coagulation tests PT and PTT have to be within normal limits, unless the patient has been therapeutically anti-coagulated for previous venous thrombosis. * Provide voluntary informed consent for Tissue Screening and Apheresis Inclusion Criteria Step 2: 1. Subject met all Step 1 Eligibility Criteria. 2. Tumor cells test positive for EGFRvIII expression (by RT-PCR, next generation sequencing, or immunohistochemistry) and a CART EGFRvIII product has been manufactured and formulated. Patients who have previously been treated with an EGFRvIII-targeted therapy and recurred are only eligible if a tumor sample obtained after their recurrence tests positive for EGFRvIII. 3. Stage of disease: * Cohort 1: Patients with first relapse of previously diagnosed primary glioblastoma. Recurrence may be determined by imaging and clinical criteria alone. * Cohort 2: Patients with newly diagnosed glioblastoma with a less than 95% resection or greater than or equal to 1 cm\^3 of residual disease on the post-operative MRI (typically post-operative day 1). 4. If the patient is on dexamethasone, the dose must be 4 mg/day or less prior to CART-EGFRvIII infusion. 5. It is anticipated that all patients in Cohort 2 will have completed standard of care external beam radiotherapy and chemotherapy with temozolomide (TMZ) at the time of the pre-infusion safety visit. 6. Life expectancy less greater than 3 months 7. ECOG performance status of 0 or 1 9\. Participants with adequate organ function as measured by: * White blood count greater than or equal to 2500/mm\^3; platelets greater than or equal to 100,000/mm\^3, hemoglobin greater than or equal to 9.0 g/dL; without transfusion or growth factor support * AST, ALT, GGT, LDH, alkaline phosphatase within 2.5 x upper normal limit, and total bilirubin less than or equal to 2.0 mg/dL * Serum creatinine less than or equal to 1.5 x upper limit of normal * Coagulation tests PT and PTT have to be within normal limits, unless the patient has been therapeutically anti-coagulated for previous venous thrombosis. * Adequate cardiac function (greater than EF 55%) 10. Provide voluntary informed consent for study treatment. 11. Female subjects of reproductive potential must agree to use a reliable method of contraception. Exclusion Criteria Step 1: * Female subjects of reproductive potential who are pregnant or lactating. Female study participants of reproductive potential must have a negative serum pregnancy test as part of Step 1 eligibility confirmation. * Uncontrolled active infection. * Active or latent chronic hepatitis B \[detectable hepatitis B surface antigen (HBsAg)\] or active hepatitis C (positive serology \[HCV Ab\]) infection. * HIV infection. * Previous treatment with any gene therapy products. * Known addiction to alcohol or illicit drugs. * History of allergy or hypersensitivity to study product excipients (human serum albumin, DMSO, and Dextran 40) Exclusion Criteria Step 2: * Female subjects of reproductive potential who are pregnant or lactating. Female study participants of reproductive potential must have a negative serum pregnancy test within two weeks prior to CART-EGFRvIII cell infusion. The safety of this therapy on unborn children is not known. * Uncontrolled active infection. * Use of immunosuppressive agents such as cyclosporine, MMF, tacrolimus, or rapamycin within 4 weeks of enrollment on Step 2. * A minimal dose of corticosteroid (dexamethasone up to 4 mg/day) is permitted. Recent or current use of inhaled steroids is not exclusionary. * Previous treatment with any gene therapy products. * Subjects or their physicians anticipate use of any of the following concurrent treatment or medications including: a. Radiosurgery (except for the Standard of Care Fractionated External Radiation therapy is a part of the protocol regimen in Cohort 2) b. Chemotherapy (except for the Standard of Care Temozolomide therapy in Cohort 2) c. Interferon (e.g. Intron-A®) d. Allergy desensitization injections e. Any ongoing investigational therapeutic medication. f. Bevacizumab * Participants who have another cancer diagnosis with history of visceral metastases at the time of pre-entry evaluation. The following diagnoses are examples that will be allowed: * squamous cell cancer of the skin without known metastasis * basal cell cancer of the skin without known metastasis * carcinoma in situ of the breast (DCIS or LCIS) * carcinoma in situ of the cervix * prostate cancer with only PSA recurrence * any cancer that has not required systemic therapy (other than hormonal therapies) for the past three (3) years. * Any uncontrolled active medical disorder that would preclude participation as outlined. * Unstable angina and/or myocardial infarction within 6 months prior to screening * Known addiction to alcohol or illicit drugs. * History of allergy or hypersensitivity to study product excipients (human serum albumin, DMSO, and Dextran 40)