Inclusion Criteria:

          -  Patients with locally advanced or metastatic chordoma with confirmed diagnosis in a
             reference pathology (with immunohistology for epithelial membrane antigen, S100,
             Brachyury, Integrase interactor 1 (INI-1)) who have no response or have lost response
             to treatment with a tyrosine kinase inhibitor e.g. imatinib, lapatinib, erlotinib,
             sunitinib, sorafenib, etc.

          -  At least one measurable tumor lesion

          -  Loss of p16 determined immunohistochemically or CDKN2A/B genomically, presence of
             CDK4/6 and RB1 determined immunohistochemically or by RNA-Sequencing.

          -  Age ≥ 18 years, no upper age limit

          -  Availability of tissue blocks preferably not older than 12 months for immunohistologic
             assessment (if no adequate material is available, re-biopsy should be considered
             before entering the study)

          -  No chemotherapy two weeks before study

          -  Non-pregnant and non-nursing. Women of child-bearing potential must have a negative
             serum or urine pregnancy test with a sensitivity of at least 25 mIU/mL within 72 hours
             prior to registration (WOCBP is defined as a sexually active mature woman who has not
             undergone a hysterectomy or who has had menses at any time in the preceding 24
             months).

          -  Women of child-bearing potential must either commit to continued abstinence from
             heterosexual intercourse or begin one acceptable method of birth control (double
             barrier contraceptive method (IUD, condome), tubal ligation, or partner's vasectomy)
             while on therapy and for 14 weeks after the last dose of therapy. Hormonal
             contraception alone is an inadequate method of birth control. Female patients must
             agree not to donate lactation during treatment and until 14 weeks after end of
             treatment.

          -  Men must agree not to father a child and must use a latex condom during any sexual
             contact with WOCBP while receiving therapy and for 14 weeks after therapy is stopped,
             even if they have undergone successful vasectomy. Sperm donation is not permitted for
             the same time interval.

          -  Signed written informed consent

          -  Performance status ≤ 2 according to Eastern Cooperative Oncology Group (ECOG) /World
             Health Organization (WHO) criteria

          -  Ability of patient to understand the character and individual consequences of clinical
             trial

        Exclusion Criteria:

          -  Prior treatment with palbociclib or known intolerance/allergy to the compound or any
             ingredient (acquired or hereditary).

          -  Co-therapy with strong/potent CYP3A inducers and/or inhibitors, (e.g., Clarithromycin,
             Indinavir, Itraconazol, Ketoconazol, Lopinavir/Ritonavir, Nefazodon, Nelfinavir,
             Posaconazol, Saquinavir, Telaprevir, Telithromycin, Voriconazol, and St. John's Wort
             [Hypericum perforatum])) while on treatment with study drug.

          -  Organ insufficiency: creatinine clearance <30ml/min; total bilirubin > 1.5x upper
             normal serum level; AST > upper normal serum level ; abnormal blood counts; heart
             failure (New York Heart Association (NYHA) III/IV); uncontrolled hypertension;
             unstable angina; serious cardiac arrhythmia; severe obstructive or restrictive
             ventilation disorder

          -  Uncontrolled infection

          -  Patients with a "currently active" second malignancy other than non-melanoma skin
             cancer. Patients are not considered to have a "currently active" malignancy if the
             patients have completed therapy and are considered by the patients physician to be at
             less than 30% risk of relapse within one year.

          -  Severe neurologic or psychiatric disorder interfering with ability of giving informed
             consent

          -  Known or suspected active alcohol or drug abuse

          -  Known positivity for HIV, active hepatitis A virus (HAV), hepatitis B virus (HBV), or
             hepatitis C virus (HCV) infection

          -  Uncontrolled central nervous system (CNS) involvement (treatment for CNS-involvement
             prior to inclusion is allowed)

          -  Cytopenia: platelets <100 G/l, neutrophils <1.0 G/l, hemoglobin <10.0 g/dl

          -  corrected QT interval (QTc) >470 msec (based on the mean value of triplicate ECGs),
             family or personal history of long or short QT syndrome, Brugada syndrome, or known
             history of QTc prolongation or Torsade de Pointes

          -  Uncontrolled electrolyte disorders that can aggravate the effects of a QTc-prolonging
             drug (e.g., hypocalcemia, hypokalemia, hypomagnesemia)

          -  Participation in other ongoing interventional clinical trials