The primary purpose of this study is to determine if the administration of a higher dose would decrease the chance of tumor recurrence, compared to the risk of tumor recurrence with a lower dose. Most of the treatment will be given protons, but participants may receive a small portion of treatment with x-rays, because less radiation is given to the skin with x-rays. This study uses two slightly different doses of radiation It is not clear at this time which of the dose levels is better.

• Participants will be assigned to a dose level by random chance, like flipping a coin.
• A treatment plan will be determined by a treatment planning CT scan and will either involve 40-44 treatments or 37-40 treatments.

Inclusion Criteria:

• Biopsy proven chordoma. Slides must be reviewed prior to randomization by the central review pathologist
• Sites: Intercranial (sphenoid, clivus, petrous, basio-occiput) or cervical spine
• Boost target volume less than or equal to 150
• 18 years of age or older
• Karnofsky Performance Status > 50
• Neurologic Function of I or II
• No evidence of metastases

Exclusion Criteria:

• Previous radiation to the head or neck that would compromise the ability to deliver the prescribed treatment
• Concurrent or prior malignancy unless disease free for 5 or more years
• Evidence of metastatic disease
• Diabetes mellitus
• Major medical illness or psychiatric impairments that in the opinion of the investigator, will prevent administration or completion of the protocol therapy