Pemetrexed for the Treatment of Chordoma

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.