This is a phase I dose escalation study of CUDC-101 in combination with concurrent cisplatin and radiation therapy in patients with locally advanced head and neck cancer. CUDC-101 is a multi-targeted agent designed to inhibit epidermal growth factor receptor (EGFR), human epidermal growth factor receptor Type 2 (Her2) and histone deacetylase (HDAC). The study is designed to establish the safety, tolerability and maximum tolerated dose (MTD) of CUDC-101 when administered in combination with concurrent cisplatin and radiation over an 8-week treatment course, consisting of a one week run-in period of CUDC-101 administered alone, followed by seven weeks of combination treatment with CUDC-101, cisplatin and radiation therapy.