The purpose of this study is to test the safety and tolerability of pemetrexed administered to people with chordoma. Other purposes of this study are to:

• find out side effects (good and bad) of pemetrexed;
• learn more about how pemetrexed might affect the growth of cancer cells;
• evaluate tumor characteristics by collecting tumor tissue samples if available;
• look at biomarkers (biochemical features that can be used to measure the progress of disease or the effects of a drug) in blood and cerebrospinal fluid if available.

This is a prospective, open-label, single-arm pilot feasibility study of pemetrexed for the treatment of adult patients with chordoma. All patients providing informed consent will be screened for eligibility. Eligible patients will receive pemetrexed by intravenous infusion on Day 1 of each 21-day treatment cycle, pre-medications (folic acid, vitamin B12, and dexamethasone), and ibuprofen if needed. Patients will continue dosing of pemetrexed until disease progression, unacceptable toxicity, withdrawal of consent, or treating physician determines it is in their best interest to stop. All patients will have regular evaluations for assessment of safety parameters and anti-tumor activity as detailed in the study flow chart.

Inclusion Criteria:

1. Participant has the ability to understand and the willingness to provide a signed and dated informed consent form.

2. Participant has the willingness to comply with all study procedures and availability for the duration of the study.

3. Participant has a diagnosis of chordoma.

4. Participant is male or female, 18 years of age or older.

5. Participant has a Karnofsky Performance Status of 50% or greater.

6. Participant has adequate organ function:

   1. ANC at least 1.5 x 10^9/L or higher
   2. Platelets at least 100 x 10^9/L or higher
   3. Hemoglobin at least 8 g/dL or higher.
   4. Total bilirubin 1.5 x upper limit of normal (ULN) or lower.
   5. ALT and AST 3 x ULN or lower.
   6. Serum creatinine 1.5 x ULN or lower.

7. Participant has the ability to interrupt non-steroidal anti-inflammatory drugs (NSAIDS) 2 days before (5 days for long-acting NSAIDs), the day of, and 2 days following administration of Pemetrexed.

8. Participant has the ability to take folic acid, Vitamin B12, and dexamethasone according to protocol.

9. Participant has recovered from any previous therapy-related toxicity to CTCAE Grade 1 or to their clinical baseline at study entry.

Exclusion Criteria:

1. Participant is less than 28 days from any investigational agent.

2. Participant has third space fluid which cannot be controlled by drainage.

3. Participant has a severe or uncontrolled medical disorder that would, in the investigator's opinion, impair ability to receive study intervention, including, but not limited to:

   1. Uncontrolled diabetes;
   2. Renal disease that requires dialysis;
   3. Pulmonary disorder requiring supplemental oxygen to keep saturation >95% and the situation is not expected to resolve within 2 weeks;
   4. Severe dyspnea at rest or requiring oxygen therapy;
   5. Interstitial lung disease;
   6. History of major surgical resection involving the stomach or small bowel;
   7. Preexisting Crohn's disease;
   8. Ulcerative colitis;
   9. Uncontrolled vasculitis and/or disease with known vasculitis;
   10. Preexisting chronic condition resulting in baseline Grade 2 or higher diarrhea;
   11. Psychiatric illness/social situations that would limit compliance with study requirements.

4. Participant has an active bacterial infection requiring intravenous [IV] antibiotics at time of initiating study treatment, fungal infection, or detectable viral infection (such as known human immunodeficiency virus positivity or with known active hepatitis B or C).

5. Participant has a personal history or presence of any of the following cardiovascular conditions:

   1. Syncope of cardiovascular etiology;
   2. Ventricular arrhythmia of pathological origin (including, but not limited to, ventricular tachycardia and ventricular fibrillation);
   3. Myocardial infraction within 6 months of investigational product administration;
   4. Unstable angina;
   5. Sudden cardiac arrest;
   6. Congestive heart failure (NYHA classification ≥ 3).

6. Participant is a female of childbearing potential who is pregnant or nursing.