-  INCLUSION CRITERIA:

          -  Patients must have histologically or cytologically confirmed locally recurrent HNSCC
             for whom re-irradiation for local control is considered standard of care. Patients
             with potentially reactive benign nodes will not be excluded.

          -  Patients with HPV-negative or HPV-positive head and neck cancer are eligible.

          -  Patients who have had prior treatment with immune therapies are eligible.

          -  Patients must have received curative-intent platinum- and/or cetuximab-based
             chemoradiotherapy.

          -  Patients must have completed their last treatment dose with chemotherapy or
             immunotherapy at least 4 weeks (6 weeks for nitrosoureas or mitomycin C) before
             enrolling on study.

          -  Patients must have completed their last treatment dose with radiotherapy at least 6
             months before enrolling on study.

          -  Patients who have had major surgery must be fully recovered and require a recovery
             period of at least 4 weeks prior to enrolling on study.

          -  Age greater than or equal to 18 years.

          -  ECOG performance status less than or equal to 2 (see Appendix A).

          -  Patients must have normal organ and marrow function as defined below:

               -  Hemoglobin greater than or equal to 10 g/dL (transfusion permitted)

               -  Absolute neutrophil count greater than or equal to 1,500/mcL

               -  Platelets greater than or equal to 75,000/mcL

               -  Total bilirubin within 1.5 x the upper limit of normal (ULN) institutional limits

               -  AST(SGOT)/ALT(SGPT) less than or equal to 2.5 (SqrRoot) institutional upper limit
                  of normal

               -  Creatinine clearance greater than or equal to 60 mL/min/1.73 m squared for
                  patients with creatinine levels above institutional normal.

          -  Patients must have a QTc less than or equal to 480 msec.

          -  Ability to understand and the willingness to sign a written informed consent document.

          -  Patients must have measurable disease.

        EXCLUSION CRITERIA:

          -  Eligibility for curative-intent surgery.

          -  More than 2 lines of palliative systemic therapy (platinum-, taxane- or cetuximabbased
             chemotherapy or immunotherapy)

          -  Patients who are receiving any other investigational agents.

          -  Patients with known brain metastases should 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 birinapant.

          -  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 birinapant 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
             birinapant, breastfeeding should be discontinued prior to enrollment.

          -  HIV positive patients on combination antiretroviral therapy are ineligible because of
             the potential for pharmacokinetic interactions with birinapant.

          -  Patients requiring the use of anti-tumor necrosis factor (anti TNF) therapies, such as
             infliximab, or patients who have received treatment with anti-TNF therapies within 5
             half-lives of the drug (48 days for infliximab, 55 days for golimumab, 70 days for
             certolizumab and adalimumab, and16 days for etanercept).

          -  Patients with previous exposure to birinapant.