There are two types of external radiation treatments; proton beam and photon beam radiation. What type of therapy participants will receive will depend upon the location of their tumor. Standard treatment would involve receiving either proton or photon radiation delivered by a three dimensional (3-D) conformal radiation technique. 3-D conformal radiation therapy is a technique where the beams of radiation used in the treatment are shaped to match the tumor in order to avoid damaging the healthy surrounding tissue. Standard treatment also may include photon radiation delivered by intensity modulated (IMRT) technique. In this research study we are using an investigational technique to deliver proton radiation therapy called intensity modulated proton radiation treatment (IMPT) which is used to target cancer while sparing healthy tissue. With IMPT (and standard IMRT), radiation intensity can be turned down during the treatment. This control over the intensity of the radiation dose has the potential to provide accuracy and allows us to more safely increase the amount of radiation delivered to the tumor. This accuracy may potentially reduce side effects that patients would normally experience with 3-D proton radiation therapy. Surgery is often an important component of the treatment for these tumors and may be integrated with the IMPT.

• Before beginning radiation therapy, the participants will have a radiation planning computed tomographic (CT) scan of the tumor site. This is considered standard of care and the doctor will use the images from this scan to plan the radiation treatment.
• Participants may also receive surgery either before or after the study radiation treatment. This surgery is also considered standard of care and would be done regardless of being in the research study.
• The IMPT technique for delivering radiation is for research purposes only. Radiation treatment to the affected tumor will be given daily, Monday through Friday.
• The following procedures will be performed once a week during treatment: assessment of nerve, neuromuscular, motor and sensory function by clinical exam and toxicity assessment.
• Participants will return for follow-up visits after completion of the radiation treatment at the following intervals: 6 weeks after completion of treatment, 6 months after treatment, every 6 months thereafter for 4 years, and then each year after for up to 15 years.

Inclusion Criteria:

• Pathological diagnosis of chondrosarcoma of the spine or sacrum or chordoma of the base of skull, spine or sacrum. Pathologic diagnosis to be confirmed at MGH or other participating institution.
• Participants need not have measurable disease. Lesion may be primary or recurrent after prior surgery. Patient tumor status: 1) Status post biopsy only and no further surgery planned, 2) Status post resection with gross residual disease, 3) Status post grossly complete research but with margins positive or close (10mm or less), 4) Status post biopsy and patient to have additional surgery and radiation
• No prior radiation treatment to the affected skull base, spine, or sacral region. Prior chemotherapy is allowed within 30 days of start of treatment
• 18 years of age or older
• ECOG Performance Status of 0, 1 or 2
• NOrmal organ and marrow function as outlined in the protocol
• No clinical, radiographic or other evidence of distant metastasis
• Women of child-bearing potential and men must agree to use adequate contraception prior to study entry and for the duration of study participation

Exclusion Criteria:

• Participants may not be receiving any other investigational agents
• Participants with metastases
• Evidence of brainstem/cord/cauda or other neuromuscular or neurosensory malfunction from causes other than effects of local tumor growth or metabolic effects of tumor
• Uncontrolled intercurrent illness including, but not limited to ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements. Disease/conditions characterized by high radiation sensitivity. These include genetic diseases, such as ataxia telangiectasia
• Pregnant women
• Individuals with a history of a different malignancy are ineligible except for the following circumstance. Individuals with a history of other malignancies are eligible if they have been disease-free for at least 5 years and are deemed by the investigator to be at low risk for recurrence of that malignancy. Individuals with the following cancers are eligible if diagnosed and treated within the past 5 years: cervical cancer in situ, and basal cell or squamous cell carcinoma of the skin.Individuals treated for localized, node-negative cancers > 2 years ago with no evidence of cancer are also considered eligible.
• HIV-positive individuals on combination antiretroviral therapy