BN Brachyury and Radiation in Chordoma

Inclusion Criteria:

* Patients must have histologically confirmed chordoma
* Patients must have measurable disease by RECIST 1.1
* Patients must be scheduled to have radiation therapy to at least 1 target lesion.
* Age ≥12 years
* Patients must have normal organ and marrow function
* Must have recovered completely from any reversible toxicity associated with recent therapy.
* There should be a minimum of 2 weeks from any chemotherapy, small molecule/targeted therapy, immunotherapy and/or radiation prior to enrolment
* Females of childbearing potential and male partners of Females of childbearing potential must agree to use effective birth control or abstinence from screening to after the last vaccination therapy

Exclusion Criteria:

* Concurrent treatment for cancer, with specific exceptions noted in the inclusion criteria
* Chronic hepatitis B or C infection.
* Any significant disease, that in the opinion of the investigator may impair the patient's tolerance of trial treatment.
* Significant dementia, altered mental status, or any psychiatric condition that would prohibit the understanding, or rendering of informed consent.
* 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.
* Concurrent use of systemic steroids, except for physiological doses of systemic steroid replacement or local steroid use.
* Patients who are receiving any other investigational agents within 28 days before start of trial treatment.
* History of allergic reactions attributed to compounds of similar chemical or biological composition to MVA-BN/FPV-Brachyury or other agents used in trial. History of allergic reactions to aminoglycoside antibiotic or egg products.
* Serious or uncontrolled intercurrent illness, included but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia or psychiatric illness/social situations that, in the opinion of the investigator, would limit compliance with trial requirements.
* Pregnant women are excluded from this trial due to the unknown effects of the BN-Brachyury on the fetus or infant.
* HIV-positive patients are ineligible because of the potential for decreased immune response to the vaccine.
* Significant cardiovascular disease, which includes but is not limited to New York Heart Association Heart Failure Class II or greater, myocardial infarction within the previous 3 months, unstable arrhythmias, unstable angina.