Toripalimab in Combination With Standard Treatment for Human Papillomavirus (HPV) Positive Throat Cancer

Inclusion Criteria: * Subjects must have pathologically confirmed HPV16-positive head and neck squamous cell carcinoma of the oropharynx. Confirmed HPV-positive disease of other subsites are uncommon but also eligible. * HPV16 subtype demonstrated based on the following guidelines: * p16 IHC positivity is sufficient to enroll and initiate treatment (p16 IHC interpretation to follow guidelines by Jordan and Lingen et al72). * HPV PCR must demonstrate HPV16 subtype. * Following p16 IHC positivity, HPV16 is to be demonstrated using HPV PCR which is anticipated to result prior to cycle 1 day 15. * Patients must be at least 18 years of age. * Subjects with AJCC (8th edition, 2018) N1 (if solitary lymph node must be \>=3cm), N2-N3 nodal disease or T3-T4 primary tumor (with any N). * Measurable disease (either primary site and/or nodal disease) by RECIST 1.1 criteria. * No previous radiation or chemotherapy for a head and neck cancer. * 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. * ECOG performance status 0-1 * Normal Organ Function per protocol criteria * Patients must be considered to be a candidate to receive cisplatin by the treating physician. * 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. * 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. * Women must not be breastfeeding. * Women of childbearing potential must agree to follow instructions for method(s) of contraception for the duration of treatment. * 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). Exclusion Criteria: * Unequivocal demonstration of distant metastatic disease (M1 disease). * Non-HPV16 subtype. * Unidentifiable primary site. * Intercurrent medical illnesses that impairs the patient's tolerance to therapy or limits 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). * Subject with low risk N1 disease (defined as single lymph node \<3cm) * Active, known, or suspected, autoimmune or inflammatory disorders requiring immunosuppressive therapy, with the exception of low-dose prednisone (\<= 10mg or equivalent). The following are exceptions to these criteria: * Patients with vitiligo or alopecia. * Patients with hypothyroidism (e.g., following Hashimoto syndrome) stable on hormone replacement. * Any chronic skin condition that does not require systemic treatment. * Treatment with immunosuppressive or replacement medication: * Immunosuppressive doses of systemic medication, such as steroids or absorbed topical steroids (doses \> 10 mg/day prednisone or equivalent), within 14 days of the first administration of study treatment. Note: inhaled or topical steroids and adrenal replacement in doses equivalent to \> 10 mg/day prednisone are permitted in the absence of active autoimmune disease. * Any chronic immunosuppressive medication within 6 months prior to the first administration of study treatment (unless agreed otherwise between the Sponsor and the Investigator on a case-by-case basis). * Active autoimmune disease that has required systemic treatment in past 2 years (i.e., with use of disease modifying agents, corticosteroids, or immunosuppressive drugs). Replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment. * Patients who have had a prior anaphylactic or other severe reaction to human immunoglobulin or antibody formulation administration. * Herbal remedies with immune-stimulating properties or known to potentially interfere with major organ function within 28 days prior to the first dose of study treatment, unless agreed otherwise with the primary investigator. * 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. * Patients receiving other investigational agents. * Prior systemic anti-cancer treatment within the last 8 weeks. * 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. * Has known history of, or any evidence of active, non-infectious pneumonitis. * Has known active Hepatitis B or hepatitis C. If eradicated, patient is eligible. * Has received a live vaccine within 28 days of planned start of study therapy.