 Researchers at the National Cancer Institute NCI are now enrolling patients in a phase 2 clinical trial to determine whether the yeast-brachyury vaccine GI-6301 improves the effectiveness of radiation for patients with localized chordoma. Chordoma patients with inoperable or residual tumor who do not have metastases and are planning to be treated with definitive 70Gy radiation are eligible to participate. Patients will initially be randomized to receive radiation plus the vaccine or radiation plus a blinded placebo. Those randomized to receive radiation plus placebo will have the option to receive vaccine if their tumor grows while on the study. The study will compare the outcomes of patients treated with radiation with and without the vaccine to determine whether the vaccine can increase the chances of shrinking the tumor andor preventing further tumor growth. 