A Study of Dostarlimab vs Placebo After Chemoradiation in Adult Participants With Locally Advanced Unresected Head and Neck Squamous Cell Carcinoma

Inclusion Criteria: Participants are eligible to be included in the study only if all of the following criteria apply: * Has newly diagnosed unresected Locally Advanced (LA) histologically confirmed HNSCC of the oral cavity, oropharynx, hypopharynx or larynx and completed cisplatin plus radiotherapy (termed "CRT" in this protocol) with curative intent and has no evidence of distant metastatic disease. * Has provided acceptable core or excisional biopsy obtained prior to CRT: * PD-L1 positive tumor status * If the primary tumor site is oropharyngeal carcinoma, the participant must have p16 immunohistochemistry (IHC) testing. * Has an Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 * Has adequate organ function. Exclusion Criteria: Participants are excluded from the study if any of the following criteria apply: * Has received prior radiation therapy (RT), systemic therapy, targeted therapy, or surgery for management of head and neck cancer not considered part of CRT. Participants receiving induction chemotherapy are excluded. CRT combinations with components other than cisplatin and RT (e.g., experimental agents, including radiosensitizers/radioprotectants, cetuximab) are not eligible. * Has cancer outside of the oropharynx, larynx, hypopharynx or oral cavity, such as nasopharyngeal, sinus, other para-nasal, or other unknown primary head and neck cancer. Has more than one primary HNSCC tumor. * Has experienced any of the following with prior immunotherapy: any immune-related adverse event (irAE) of Grade ≥3, immune-related severe neurologic events of any grade (e.g., myasthenic syndrome/myasthenia gravis, encephalitis, Guillain-Barré Syndrome, or transverse myelitis), exfoliative dermatitis of any grade (Stevens-Johnson Syndrome, toxic epidermal necrolysis, or Drug Rash with Eosinophilia and Systemic Symptoms \[DRESS\] syndrome), or myocarditis of any grade. Non-clinically significant laboratory abnormalities are not exclusionary. * Has undergone any major surgical procedure or experienced significant traumatic injury that has not resolved by the time of randomization. * Has any history of interstitial lung disease or pneumonitis (past or current). * Has cirrhosis of any stage or current unstable liver biliary disease per investigator assessment defined by the presence of ascites, encephalopathy, coagulopathy, hypoalbuminemia, esophageal/gastric varices, or persistent jaundice. * Has a history or current evidence of any medical condition, therapy, or laboratory abnormality that might confound the study results, interfere with their participation for the full duration of the study intervention, or indicate it is not in the best interest of the participant to participate, in the opinion of the investigator. * Is receiving any other anticancer or experimental therapy. No other experimental therapies (including but not limited to chemotherapy, radiation, hormonal treatment, antibody therapy, immunotherapy, gene therapy, vaccine therapy, or other experimental drugs) of any kind are permitted while the participant is receiving study intervention. * Previous treatment with anti-PD-1, anti-PD-L1, or anti-PD-L2 agent or an agent directed to another stimulatory or coinhibitory T-cell receptor \[e.g., Cytotoxic T-lymphocyte associated protein 4 (CTLA4), OX-40, CD137\] * Is pregnant, breastfeeding, or expecting to conceive children within the projected duration of the study, starting with the Screening Visit through 120 days after the last dose of study intervention. * Has a history of severe allergic and/or anaphylactic reactions to chimeric, human or humanized antibodies, fusion proteins, or known allergies to dostarlimab or its excipients.