This study is looking to see if nivolumab, an immunotherapy drug, given with carboplatin and paclitaxel (2 chemotherapy agents) during induction therapy in advanced stage HPV negative patients can significantly shrink the subject's cancer.

Inclusion Criteria:

1. Patients must have pathologically confirmed locally advanced, non-metastatic, HPV-negative head and neck squamous cell carcinoma of the oral cavity, oropharynx, hypopharynx, nasopharynx, larynx, or sinuses.

2. Stage IV disease with the exception of nasopharyngeal tumor-3, node-2 (stage III) based of American Joint Committee on Cancer staging 8th edition

3. If a primary oropharyngeal squamous cell carcinoma is diagnosed, HPV must be ruled out by immunohistochemistry.

4. Availability of ≥10 unstained 5 micron slides. Patients who cannot fulfill this requirement will need to undergo a new biopsy prior to enrollment on study.

5. Patients must be at least 18 years of age.

6. Measurable disease (either primary site and/or nodal disease) by RECIST criteria.

7. No previous radiation or chemotherapy for a head and neck cancer.

8. No complete 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/excision of the tumor with residual measurable disease is acceptable.) No surgical procedures or biopsies will occur after baseline scans are performed and measurable lesions are identified.

9. Eastern Cooperative Oncology Group performance status 0-1

10. Normal Organ Function

    1. Leukocytes ≥ 3000/mm3
    2. Platelets ≥ 100,000/mm3
    3. Absolute neutrophil count ≥ 1,500
    4. Hemoglobin ≥ 9.0 gm/dL
    5. Aspartate Aminotransferase (AST) and Alanine Aminotransferase (ALT) ≤ 2.5x upper limit of normal
    6. Alkaline phosphatase ≤ 2.5x upper limit of normal
    7. Albumin > 2.9 gm/dL
    8. Total bilirubin ≤ 1.5 mg/dL
    9. Creatinine clearance > 45 mL/min, normal within 2 weeks prior to start of treatment (Of note, the standard Cockcroft and Gault formula must be used to calculate creatinine clearance (CrCl) for enrollment or dosing)

11. 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.

12. Women of childbearing potential must have a negative serum or urine pregnancy test (minimum sensitivity 25 IU/L or equivalent units of HCG) within 24 hours prior to the start of study drug

13. Women must not be breastfeeding

14. Women of childbearing potential must agree to follow instructions for method(s) of contraception for the duration of treatment with study drug(s) plus 6 months after completing chemoradiation or receiving the last dose of consolidative nivolumab, whichever occurs latest.

15. Men who are sexually active with women of childbearing potential must agree to follow instructions for method(s) of contraception for the duration of treatment with study drug(s) plus 6 months after completing chemoradiation or receiving the last dose of consolidative nivolumab, whichever occurs latest.

Exclusion Criteria:

1. Unequivocal demonstration of distant metastatic disease (M1 disease).
2. Unidentifiable primary site.
3. Inter-current medical illnesses which would impair patient tolerance to therapy or limit survival. This includes but is 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. Patients with clinically stable and/or chronically managed medical illnesses that are not symptomatic and/or are not expected to impact treatment on protocol are still eligible (conditions to be reviewed by the PI to confirm eligibility)
4. Prior surgical therapy other than incisional/excisional biopsy or organ-sparing procedures such as debulking of airway-compromising tumors. Residual measurable tumor is required for enrollment as discussed above.
5. Patients receiving other investigational agents.
6. Diagnosis of immunodeficiency or is receiving systemic steroid therapy in excess of physiologic dose or any other form of immunosuppressive therapy within 7 days prior to the first dose of trial treatment.
7. Known history of active tuberculosis (Bacillus Tuberculosis infection).
8. Hypersensitivity to nivolumab or any other drug used in this protocol.
9. Prior systemic anti-cancer treatment within the last 8 weeks.
10. Has a known additional malignancy that is progressing or requires active treatment. Exceptions include basal cell carcinoma of the skin or squamous cell carcinoma of the skin that has undergone potentially curative therapy or in situ cervical cancer or any tumors that are not likely to influence life expectancy in the subsequent 3 years without active treatment.
11. Has active autoimmune disease that has required systemic therapy in the past year (i.e. with steroids or immunosuppressive drugs). Replacement therapy e.g. levothyroxine, insulin, or physiologic corticosteroid doses for adrenal or pituitary insufficiency, etc. are not considered a form of systemic treatment.
12. Has known history of, or any evidence of active, non-infectious pneumonitis.
13. Has a history of HIV.
14. Has known active Hepatitis B or hepatitis C. If eradicated, patient is eligible.
15. Has received a live vaccine within 28 days of planned start of study therapy.