Inclusion Criteria:

          -  Patients must have pathologically confirmed HPV-positive squamous cell carcinoma

          -  HPV testing must follow the following criteria

               -  HPV testing using an E6/E7 based assay is preferred, and does not require any
                  validation (e.g. HPV in situ hybridization [ISH] or HPV E6/E7 polymerase chain
                  reaction [PCR])

               -  For oropharyngeal tumors p16 immunohistochemistry (IHC) positivity is sufficient
                  to enroll and initiate treatment (p16 IHC interpretation to follow guidelines by
                  Jordan/Lingen et al 2012); it is recommended that p16 IHC positivity is validated
                  at a later point (during or after treatment) using an E6/E7 based test at the
                  University of Chicago and provided slides will be used

               -  For non-operative (OP) tumors accurate HPV testing (i.e. ISH, or E6/E7 based
                  testing) is required for enrollment and treatment initiation

          -  Availability of >= 10 unstained 5 micron slides

          -  Patients with American Joint Committee on Cancer (AJCC) (7th edition, 2010) nodal
             stage N2 or N3 or a T4 primary tumor

          -  The primary and nodal involvement must be assessable on clinical exam (mucosal and
             lymph node exam)

          -  The primary and nodal involvement must have been defined bi- or uni-dimensional
             measurements measurable by RECIST

          -  No previous radiation or chemotherapy for a head and neck cancer

          -  No surgical resection for a head and neck cancer within 8 weeks of enrollment
             (although lymph node biopsy including excision of an individual node with presence of
             residual nodal disease, or surgical biopsy of the tumor is acceptable)

          -  Eastern Cooperative Oncology Group (ECOG) performance status 0-1 (Karnofsky >= 70%)

          -  Leukocytes >= 3000/mm^3

          -  Platelets >= 100,000/mm^3

          -  Absolute neutrophil count >= 1,500

          -  Hemoglobin > 9.0 gm/dL

          -  Albumin > 2.9 gm/dL

          -  Total bilirubin =< 1.5 mg/dl

          -  Creatinine clearance > 45 mL/min (or serum creatinine [SCr] =< 1.5 mg/dL), normal
             within 2 weeks prior to start of treatment

          -  The standard Cockcroft and Gault formula or the measured glomerular filtration rate
             must be used to calculate creatinine clearance (CrCl) for enrollment or dosing

          -  Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =< 2.5 X upper
             limit of normal (ULN)

          -  Alkaline phosphatase =< 2.5 X ULN

          -  Patients must sign a study-specific informed consent form prior to study entry;
             patients should have the ability to understand and the willingness to sign a written
             informed consent document

        Exclusion Criteria:

          -  Unequivocal demonstration of distant metastases (M1 disease)

          -  Intercurrent medical illnesses which would impair patient tolerance to therapy or
             limit survival; including but not limited to ongoing or active infection,
             immunodeficiency, symptomatic congestive heart failure, pulmonary dysfunction,
             cardiomyopathy, unstable angina pectoris, cardiac arrhythmia or psychiatric
             illness/social situations that would limit compliance

          -  Pregnant and nursing women are excluded; men and women of child-bearing potential are
             eligible but must consent to using effective contraception during therapy and for at
             least 3 months after completing therapy; women with child-bearing potential must have
             a negative serum or urine beta-human chorionic gonadotropin (B-hCG) pregnancy test at
             screening

          -  Other coexisting malignancies or malignancies diagnosed within the previous 3 years no
             evidence of disease for at least 3 years; exceptions to this include non-melanoma skin
             cancer, cervical cancer in situ, well differentiated thyroid cancer or prostate
             cancer; other cancers that per assessment of the PI are not prognosis limiting can be
             allowed after review by the PI

          -  Prior surgical therapy other than incisional or excisional biopsy and organ-sparing
             procedures such as debulking of airway-compromising tumors or neck dissection in a
             patient with an unknown primary tumor; residual tumor is required for enrollment on
             study

          -  Patients receiving other investigational agents

          -  Peripheral neuropathy >= grade 1