Vorinostat in Combination With Chemoradiation in Locally Advanced HPV Negative HNSCC

Inclusion Criteria: * Subjects must have histologically or cytologically confirmed stage III or IV HPV negative squamous cell carcinoma of the oral cavity, oropharynx or hypopharynx, tumors is deemed to be either unresectable or locally advanced. * Subjects must have received no prior therapies (chemotherapy or radiotherapy) for this disease * Age \>18 years. Because the low occurrence of HNSCC in the pediatric population, children are excluded from this study * ECOG Performance status ≤ 2 * Subjects must have normal organ and marrow function as defined below * Hemoglobin ≥ 9.0 g/dl (transfusion permitted) * Leukocytes ≥ 3,000/mcL * Absolute neutrophil count ≥ 1,500/mcL * Platelet count ≥ 100,000/mcL * Total bilirubin within normal institutional limits * AST (SGOT) ≤ 2.5 X institutional upper limit of normal * ALT (SGPT) ≤ 2.5 X institutional upper limit of normal * Serum Creatinine clearance (\> 50 ml/min) * Based on findings from animal studies and its mechanism of action, vorinostat can cause fetal harm when administered to a pregnant woman. There are insufficient data on vorinostat use in pregnant women to inform a drug-associated risk of major birth defects and miscarriage. In animal reproduction studies, vorinostat crossed the placenta and caused adverse developmental outcomes at exposures approximately 0.5 times the human exposure based on AUC0-24 hours. For this reason, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) beginning at study entry and for the duration of study participation. Male study participants should use an additional barrier method of contraception for 30 days following the last dose of vorinostat. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. * Patients must have measurable disease, per RECIST 1.1 * Subjects must have the ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Eligibility for curative-intent surgery, previous chemotherapy. * Subjects receiving any other investigational agents. * Subjects with untreated brain metastases/CNS disease will be excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events. * History of allergic reactions attributed to compounds of similar chemical or biologic composition to vorinostat. * Patients with previous exposure to vorinostat. * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements. * Subjects with uncontrolled intercurrent illness including, but not limited to ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements. * Pregnant women are excluded from this study because vorinostat may have potential for teratogenic or abortifacient effects. Because there is an unknown, but potential risk for adverse events in nursing infants secondary to treatment of the mother with vorinostat, breastfeeding should be discontinued if the mother is treated with vorinostat. These potential risks may also apply to other agents used in this study. * HIV-positive subjects on combination antiretroviral therapy are ineligible because of the potential for pharmacokinetic interactions with vorinostat. In addition, these subjects are at increased risk of lethal infections when treated with marrow suppressive therapy. Appropriate studies will be undertaken in subjects receiving combination antiretroviral therapy when indicated. Also include whether HIV testing is required for this study, or only if a known diagnosis will be excluded.