Pharmacodynamic Study to Assess the Anti-proliferative Activity of the PARP Inhibitor Olaparib in Patients With HPV Positive and HPV Negative HNSCC

Inclusion Criteria:

* Histologically confirmed HNSCC with surgically resectable disease
* No prior chemotherapy or radiation therapy as treatment for the observed HNSCC
* Patients must provide written informed consent
* Age \>=18 years of age
* Eastern Cooperative Oncology Group (ECOG) Performance Status score of \<2
* Normal organ and bone marrow function measured within 28 days prior to administration of study treatment as defined below:
* Hemoglobin \>= 10 g/dL and no blood transfusions in the 28 days prior to entry/randomization
* Absolute neutrophil count \>=1.5 x 10\^9/L
* No features suggesting of MDS/AML on peripheral blood smear
* White blood cells \> 3 x 10\^9/L
* Platelet count \>= 100 x 10\^9/L
* Total bilirubin \<= 1.5 x institutional upper limit of normal (ULN)
* AST (SGOT)/ALT (SGPT) \< 2.5 x institutional upper limit of normal unless liver metastases are present in which case it must be \< 5x ULN
* Serum creatinine \<= 1.5 x institutional ULN OR creatinine clearance \>= 50 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal
* Women of child-bearing potential must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of the study participation and must have negative serum or urine pregnancy test within 1 week prior to beginning treatment on this trial
* Must be abler to understand and sign a written informed consent document

Exclusion Criteria:

* Patients with known brain metastases. Patients may have received WBRT within 14 days or focal radiation within 1 week of cycle 1, day 1. The patient can receive a stable dose of corticosteroids before and during the study as long as these were started at least 28 days prior to treatment
* Women must not be pregnant or breastfeeding
* Patients with known hypersensitivity to olaparib or any of the excipients of the product
* Patients receiving any other investigational agents within 4 weeks of starting the study
* Involvement in the planning and/or conduct of the study
* Any previous treatment with a PARP inhibitor, including olaparib
* Concomitant use of known CYP3A4 inhibitors such as ketoconazole, itraconazole, ritonavir, indinavir, saquinavir, telithromycin, clarithromycin, and nelfinavir
* Persistent toxicities (\>=CTCAE grade 2)
* Resting ECG with QTC \>470msec on 2 or more time points within a 24 hour period or family history of long QT syndrome
* Blood transfusions within 1 month prior to study start
* Patients with myelodysplastic syndrome/acute myeloid leukemia
* Major surgery within 14 days of starting study treatment and patients must have recovered from any effects of any major surgery
* Patients considered a poor medical risk due to a serious, uncontrolled medical disorder, non-malignant systemic disease or active, uncontrolled infection.
* Unable to swallow oral medication
* Immunocompromised patients, e.g., patients who are known to be serologically positive for HIV and are receiving antiviral therapy
* Known active hepatic disease
* Uncontrolled seizures
* Previous cancer, except: adequately treated non-melanoma skin cancer, curatively treated in-situ cancer of the cervix, or other solid tumors curatively treated with no evidence of disease for 5 years
* Currently on warfarin(subcutaneous heparin is permitted)