In chordoma cell lines and patient biopsies, the p16 (CDKN2A) tumor suppressor is consistently deleted. Thus, chordomas are an example of a tumor with universal activation of the cyclin-dependent kinases 4 and 6 (CDK4/6) pathway, and experiments with patient-derived chordoma cell lines demonstrate aberrant CDK4/6 activity downstream of p16 loss can be efficiently inhibited by the CDK4/6 inhibitor palbociclib, resulting in reduced proliferation and growth of neoplastic cells. The investigators aim to conduct a phase II clinical trial to evaluate the efficacy of the small-molecule CDK4/6 inhibitor palbociclib in patients with locally advanced/metastatic chordoma who are not candidates for standard therapy. The primary objective is disease control in patients with chordoma treated with palbociclib as single agent. The study design of this phase II study is based on a Simon two-stage design.