Inclusion Criteria:

- AJCC stage III/IVB, excluding T1N1, histologically or cytologically confirmed
squamous cell carcinoma or undifferentiated carcinoma of the head and neck. Patients
should not have distant metastasis. Primary sites include: oropharynx, hypopharynx,
larynx

- Patients must have high or intermediate risk disease, defined as follows:

High risk: p16- Intermediate risk: p16+, ≥ 10 pack-year tobacco exposure
and ≥ N2 disease.

- Patients must have measurable disease, defined as at least one lesion that can be
accurately measured in at least one dimension (longest diameter to be recorded for
non-nodal lesions and short axis for nodal lesions) as >20 mm with conventional
techniques or as >10 mm with spiral CT scan, MRI, or calipers by clinical exam. See
Section 11 for the evaluation of measurable disease.

- Patients should be newly diagnosed HNSCC, with no prior therapy for this disease.

- Age >18 years.

- ECOG performance status typically <1 (Karnofsky >70%)

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

leukocytes >3,000/mcL absolute neutrophil count>1,200/mcL platelets >75,000/mcL total
bilirubin ≤ 2 mg/dL (≤ 3 mg/dL in case of gilbert's syndrome) AST/ALT ≤ 2 times
institutional ULN creatinine clearance >40 mL/min/1.73 m2

- Patients must have the ability to understand and to sign written informed consent.

Exclusion Criteria:

- Patients who have had prior chemotherapy, radiotherapy, or surgery with curative
intent for HNSCC.

Patients with a history of prior treatment with ipilimumab, anti-PD 1 antibody, CD137
agonist or other immune activating therapy such as anti-CD 40 antibody.

- Patients who are receiving any other investigational agents.

- Autoimmune disease: Patients with a history of inflammatory bowel disease, including
ulcerative colitis and Crohn's Disease, are excluded from this study, as are patients
with a history of symptomatic non-gastrointestinal autoimmune disease (e.g.,
rheumatoid arthritis, systemic progressive sclerosis [scleroderma], systemic lupus
erythematosus, autoimmune vasculitis [e.g., Wegener's Granulomatosis]); CNS or motor
neuropathy considered of autoimmune origin (e.g. Guillain-Barre Syndrome and
Myasthenia Gravis, multiple sclerosis.).

- Patients with known immunodeficiency disorder, or presumed to be unable to respond to
anti-CTLA4 mAb

- Patients with distant metastatic disease (stage IVC).

- History of allergic reactions attributed to compounds of similar chemical or biologic
composition to cetuximab or ipilimumab.

- Patient is < 2 years free from a second primary malignancy unless the other
malignancy is non-melanomatous skin cancer or an in-situ tumor treated with curative
intent.

- 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. Patients with chronic Hepatitis B or hepatitis C infections are
excluded because of potential effects on immune function and/ or drug interactions,
as well as the potential for confounded interpretation of immune-related adverse
events such as hepatic inflammation occurring on protocol.

- Pregnant women are excluded from this study because ipilimumab may have the potential
for teratogenic or abortifacient effects. These potential risks may also apply to
other agents used in this study.

- HIV-positive patients on combination antiretroviral therapy are ineligible because of
the potential for pharmacokinetic interactions with ipilimumab and immunosuppressed
individuals. Appropriate studies will be undertaken in patients receiving
combination antiretroviral therapy when indicated.