Study of Imatinib, a Platelet-derived Growth Factor Receptor Inhibitor, and LBH589, a Histone Deacetylase Inhibitor, in the Treatment of Newly Diagnosed and Recurrent Chordoma

Inclusion Criteria: * Patients greater than or equal to 18 years of age. * Histologically documented diagnosis of chordoma * At least one measurable site of disease (as defined by Response Evaluation Criteria in Solid Tumors, see Appendix 3). * Performance status 0,1, or 2 (ECOG) (see Section 6) * Patients must have adequate bone marrow and end organ function, as defined as the following: 1. WBC \> 3.0 x 109/L 2. ANC \> 1.5 x 109/L, 3. Platelets \> 100 x 109/L 4. Hemoglobin \> 10 gm/dl 5. Total bilirubin \< 1.5 x ULN (Does not apply to patients with isolated hyperbilirubinemia (e.g., Gilbert's disease) grade \<3. 6. AST/SGOT and ALT/SGPT \< 2.5 x UNL 7. Serum creatinine ≤ 2.5 x ULN or 24 hr creatinine clearance ≥ 50ml/min 8. Serum albumin ≤ 3g/dL 9. Serum amylase and lipase ≤ 1.5 x ULN 10. Alkaline phosphatase ≤ 2.5 x ULN 11. Patients must have the following laboratory values (WNL = within normal limits at the local institution lab) or corrected to within normal limits with supplements prior to the first dose of study medication: 1. Potassium (WNL) 2. Magnesium (WNL) 3. Phosphorus (WNL) 4. Calcium (WNL) * Female patients of childbearing potential must have negative pregnancy test within 7 days before initiation of study drug dosing. Postmenopausal women must be amenorrheic for at least 12 months to be considered of non-childbearing potential. Female patients of reproductive potential must agree to employ an effective barrier method of birth control throughout the study and for up to 3 months following discontinuation of study drug. * A scan should be performed within 14 days prior to registration. The same type of scan, i.e., MRI or CT must be used throughout the period of protocol treatment for tumor measurement. * Patients must have an interval of greater than or equal to 3 months from the completion of radiation therapy to study entry. * Patients must be willing to participate in the pharmacokinetic studies. * Written, voluntary informed consent. Exclusion Criteria: * Patient has received any other investigational agents within 28 days of first day of study drug dosing for treatment of chordoma, unless the disease is rapidly progressing. Patients who have been previously treated with imatinib or LBH589 are ineligible. * Patients must not be on enzyme inducing anticonvulsants or valproic acid, a seizure medication with HDAC inhibition activity. * Patient is \< 5 years free of another primary malignancy except: if the other primary malignancy is not currently clinically significant nor requiring active intervention, or if other primary malignancy is a basal cell skin cancer or a cervical carcinoma in situ. Existence of any other malignant disease is not allowed. * Patient with Grade III/IV cardiac problems as defined by the New York Heart Association Criteria. (i.e., congestive heart failure, myocardial infarction within 6 months of study) * Impaired cardiac function including any one of the following: 1. Inability to monitor the QT/QTc interval on ECG 2. Long QT syndrome or a known family history of long QT syndrome. 3. Clinically significant resting brachycardia (\<50 beats per minute) 4. QTc \> 450 msec on baseline ECG (using the QTcF formula). If QTcF \>450 msec and electrolytes are not within normal ranges, electrolytes should be corrected and then the patient re-screened for QTc 5. Myocardial infarction within 12 months prior to starting study 6. Other clinically significant uncontrolled heart disease (e.g. unstable angina, congestive heart failure or uncontrolled hypertension) 7. History of or presence of clinically significant ventricular or atrial tachyarrhythmias * Female patients who are pregnant or breast-feeding. * Patient has a severe and/or uncontrolled medical disease (i.e., uncontrolled diabetes, chronic renal disease, or active uncontrolled infection). * Patient has known chronic liver disease (i.e., chronic active hepatitis, and cirrhosis). * Patient has known brain metastasis * Patient has a known diagnosis of human immunodeficiency virus (HIV) infection. * Patient received chemotherapy within 4 weeks (6 weeks for nitrosourea or mitomycin-C)prior to study entry, unless the disease is rapidly progressing. * Patient receiving concurrent treatment with warfarin. * Patient previously received radiotherapy to \> 25 % of the bone marrow * Patient had a major surgery within 2 weeks prior to study entry. * Patient with any significant history of non-compliance to medical regimens or with inability to grant reliable informed consent. * Patients may not be receiving any other investigational agents. * History of allergic reactions attributed to compounds of similar chemical or biologic composition to imatinib or LBH589 used in study.