Chordoma is a rare bone tumor with slow growth. The standard treatment is en bloc excision, but the site of origin of the disease often prevents complete surgery. For these patients, debulking surgery followed by radiation therapy (RT) or high-dose RT alone can be an alternative. However, local relapses or more rarely metastatic disease frequently occur, and there is no efficient standard systemic therapy available. Only very limited responses are seen with chemotherapy or targeted agents, such as imatinib and lapatinib. 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 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. This trial will establish whether the overreliance of chordomas on the activation of the CDK4/6-Retinoblastoma 1 (RB1) pathway can be exploited for therapeutic benefit. Based on previous experience with 125 mg palbociclib once daily for 21 days followed by 7 days of rest in patients with breast cancer, liposarcoma, non-small cell lung cancer, hepatocellular carcinoma, ovarian cancer, mantle-cell lymphoma, and glioblastoma, this regimen is chosen. Based on a Simons optimal two-stage design the disease control rate (DCR) will be the primary end-point, whereby response is defined as complete response (CR), partial response (PR), or stable disease (SD) according to RECIST v1.1 criteria after six cycles. For sample size calculation the investigators estimate a poor response with 10% and a good response with 25% (power, 80%; alpha, 5%) leading to a first stage of 18 patients and, if three or more patients responded to a second stage with additional 25 patients (total n=43).