QUILT-3.011 Phase 2 Yeast-Brachyury Vaccine Chordoma

* INCLUSION CRITERIA: Participants must meet the following criteria for participation: 1. Diagnosis: Patients must have histologically confirmed chordoma by the Laboratory of Pathology, NCI, which is localized (no evidence of metastatic disease), unresectable and they must have planned radiation therapy, to at least one targeted lesion with evidence of growth prior to enrollment. The tentative radiation plan at enrollment must be in compliance with the required radiation doses. This can be given in standard or hypofractionated dosing with any technique deemed most appropriate by the treating radiation oncologist if other requirements are not met. 2. Patients must have disease that is measurable by RECIST version 1.1. 3. Fresh or archived tumor specimen must be available for correlative studies. 4. Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 2 at study entry (Karnofsky greater than or equal to 70) 5. Age greater than or equal to 18 years. Because no dosing or adverse event data are currently available on the use of GI-6301 (Yeast Brachyury vaccine) in patients \<18 years of age, children are excluded from this study, but will be eligible for future pediatric trials. 6. Prior Therapy: Patients must have fully recovered from prior surgery before enrollment. Prior radiation therapy is allowed provided the radiation field can safely irridated in the opinion of the treating radiation oncologist. 7. Patients must have normal organ and marrow function as defined below: * Serum creatinine less than or equal to 1.5 X upper limit of normal OR creatinine clearance on a 24-h urine collection of greater than or equal to 60 mL/min. * ALT and AST less than or equal to 3 X the upper limits of normal. * Total bilirubin less than or equal to 1.5 X upper limit of normal OR in patients with Gilbert s syndrome, a total bilirubin less than or equal to 3.0. * Hematological eligibility parameters (within16 days of starting therapy): Granulocyte count greater than or equal to 1,500/mm3 Platelet count greater than or equal to 100,000/mm3 8. Men and women of child-bearing potential must agree to use effective birth control or abstinence during and for a period of 4 months after the last vaccination therapy. 9. Patients must not have a history of yeast allergy. If patient has a questionable history of allergy to yeast, a yeast skin test can be performed. Patients would be eligible if skin test is negative. 10. Ability to understand and the willingness to sign a written informed consent document. EXCLUSION CRITERIA: Patients with any of the following will not be eligible for participation in this study: 1\. Patients should have no evidence of immune dysfunction as listed below. * Human immunodeficiency virus (HIV) positivity due to the potential for decreased immune response to the vaccine. * Active autoimmune diseases requiring treatment or a history of autoimmune disease that might be stimulated by vaccine treatment. This requirement is due to the potential risks of exacerbating autoimmunity. However, patients with vitiligo, diabetes mellitus, and Hashimoto thyroiditis on appropriate replacement therapy may be enrolled. * History of allergy or untoward reaction to yeast-based products (any hypersensitivity to yeast-based products will be excluded). * Pregnant or breast-feeding women, due to the unknown effects of the Yeast-brachyury vaccine on the fetus or infant. * Serious intercurrent medical illness which would interfere with the ability of the patient to carry out the treatment program, including, but not limited to, inflammatory bowel disease, Crohn's disease, ulcerative colitis, or active diverticulitis. * Chronic hepatitis infection, including B and C, because potential immune impairment caused by these disorders may diminish the effectiveness of this immunologic therapy. * Any significant disease that, in the opinion of the investigator, may impair the patient s tolerance of study treatment. * Significant dementia, altered mental status, or any psychiatric condition that would prohibit the understanding or rendering of informed consent. * Patients may not be on systemic steroids within 4 weeks of enrolling on study with the exception of physiologic replacement doses (for instance in the case of adrenal insufficiency) or steroid premedication for baseline MRI and/or CT in the case of subjects with known contrast dye allergies.