Inclusion Criteria:  Age >= 12 years Histologically confirmed diagnosis of chordoma which is advanced (unresectable) and/or metastatic Eastern Cooperative Oncology Group (ECOG) performance status of =< 2 At least one site of measurable disease on x-ray/computed tomography (CT)/ magnetic resonance imaging (MRI) and/or positron emission tomography (PET)/CT scan as defined by RECIST 1.1 criteria. Baseline imaging must be performed within 30 days of day 1 of study Absolute neutrophil count (ANC) >= 1000/uL (within 28 days of day 1 of study) Hemoglobin >= 9 g/dL (5.58 mmol/L) (within 28 days of day 1 of study) Platelets >= 100,000/uL (within 28 days of day 1 of study) Total bilirubin =< 1.5 mg/dL (25.65 umol/L) (NOTE: Patients with elevated bilirubin secondary to Gilbert's disease are eligible to participate in the study) (within 28 days of day 1 of study) Aspartate transaminase (AST) and alanine transaminase (ALT) =< 3.0 times the upper limit of normal (ULN; or 5.0 times the ULN in the setting of liver metastases) (within 28 days of day 1 of study) Serum creatinine =< 1.5 times the ULN, or creatinine clearance (measured via 24-hour urine collection) >= 40 mL/minute (that is, if serum creatinine is > 1.5 times the ULN, a 24-hour urine collection to calculate creatinine clearance must be performed) (within 28 days of day 1 of study) Patients may have any prior line of therapy, but there should a washout period of at least 3 weeks from any systemic therapy (small molecule/targeted agents, immunotherapies) and/or radiation therapy Patients should be completely recovered from any reversible toxicities associated with any prior therapies There should be access of archival tumor tissue for central pathology review, or a new tumor related biopsy should be considered within acceptable risk to the patient Patients must have no prior history of use of an EGFR inhibitor for treatment of their chordoma Because the teratogenicity of cetuximab is not known, the patient, if sexually active, must be postmenopausal, surgically sterile, or using effective contraception (hormonal or barrier methods. Women of childbearing potential include pre-menopausal women and women within the first 2 years of the onset of menopause. Women of childbearing potential must have a negative serum pregnancy test =< seven days prior to day 1 of study Life expectancy of > 3 months  Exclusion Criteria:  Prior use of an EGFR inhibitor for treatment of their chordoma Non-metastatic, resectable disease No measurable disease according to RECIST 1.1 Life expectancy of less than 3 months Other invasive malignancy within 2 years except for noninvasive malignancies such as cervical carcinoma in situ, non-melanomatous carcinoma of the skin or ductal carcinoma in situ of the breast that has/have been surgically cured Concomitant participation to another clinical trial with active agent during the study (concomitant non-interventional study will be allowed) Patients who have a history of allergic reactions attributed to compounds of chemical or biologic composition similar to those of cetuximab  Patients with severe and/or uncontrolled concurrent medical disease that in the opinion of the investigator could cause unacceptable safety risks or compromise compliance with the protocol  The patient has clinically relevant coronary artery disease or history of myocardial infarction in the last 12 months or high risk of uncontrolled arrhythmia or uncontrolled cardiac insufficiency The patient has uncontrolled or poorly-controlled hypertension (>180 mmHg systolic or > 130 mmHg diastolic) Major surgery within 4 weeks prior to day 1 of study or who have not recovered adequately from prior surgery Patients who have received wide field radiotherapy =< 3 weeks or limited field radiation for palliation < 3 weeks prior to day 1 of study or who have not recovered adequately from side effects of such therapy Patients who have received any prior systemic therapy < 3 weeks prior to day 1 of study or have not recovered adequately from toxicities to the baseline Women who are pregnant or nursing/breastfeeding Inability to comply with protocol required procedures