Study of Pembrolizumab With Concurrent Chemoradiation Therapy Followed by Pembrolizumab With or Without Olaparib in Stage III Non-Small Cell Lung Cancer (NSCLC) (MK-7339-012/KEYLYNK-012)

Inclusion Criteria: * Has pathologically (histologically or cytologically) confirmed diagnosis of NSCLC * Has Stage IIIA, IIIB, or IIIC NSCLC by American Joint Committee on Cancer Version 8 * Is unable to undergo surgery with curative intent for Stage III NSCLC * Has no evidence of metastatic disease indicating Stage IV NSCLC * Has measurable disease as defined by RECIST 1.1 * Has not received prior treatment (chemotherapy, targeted therapy or radiotherapy) for Stage III NSCLC; participants who have received neoadjuvant and/or adjuvant therapy for early stage disease are not eligible * Has provided a tumor tissue sample (tissue biopsy \[core, incisional, or excisional\]) * Has an Eastern Cooperative Oncology Group (ECOG) Performance Status of 0 or 1 assessed within 7 days prior to the first administration of study intervention * Has a life expectancy of at least 6 months * A male participant must agree to use contraception and refrain from donating sperm during the intervention period and for at least the time needed to eliminate each study intervention after the last dose of study intervention unless confirmed to be azoospermic (vasectomized or secondary to medical cause). The length of time required to continue contraception for each study intervention is as follows: Olaparib, platinum doublet, and radiotherapy: 90 days * A female participant is eligible to participate if she is not pregnant, not breastfeeding, and agrees to use contraception and refrain from donating eggs (ova, oocytes) to others or freeze/store for her own use for the purpose of reproduction during the treatment period and for at least the time needed to eliminate each study intervention after the last dose of study intervention and agrees to abstain from breastfeeding during the study intervention period and for at least 120 days after the last dose of study intervention. The length of time required to continue contraception for each study intervention is as follows: Pembrolizumab: 120 days; Olaparib, platinum doublet, and radiotherapy: 180 days * Has a negative highly sensitive pregnancy test (\[urine or serum\] as required by local regulations) within 24 hours for urine or within 72 hours for serum before the first dose of study intervention. If a urine test cannot be confirmed as negative (e.g., an ambiguous result), a serum pregnancy test is required. In such cases, the participant must be excluded from participation if the serum pregnancy result is positive. * Has had her medical history, menstrual history, and recent sexual activity reviewed by the investigator to decrease the risk for inclusion of a woman with an early undetected pregnancy. * Has adequate pulmonary function tests * Has adequate organ function * Has provided written informed consent Exclusion Criteria: * Has small cell lung cancer or a mixed tumor with presence of small cell elements * Has myelodysplastic syndrome (MDS)/acute myeloid leukemia (AML) or has features suggestive of MDS/AML * Has had documented weight loss \>10% (from baseline) in the preceding 3 months * Has received prior radiotherapy to the thorax, including radiotherapy to the esophagus, mediastinum, or for breast cancer * Has received prior therapy with an anti-programmed cell death 1 (ant-PD-1), anti-programmed cell death ligand 1 (anti-PD-L1), or anti- programmed cell death ligand 2 (anti-PD-L2) agent or with an agent directed to another stimulatory or co-inhibitory T-cell receptor * Has received prior therapy with olaparib or with any other polyadenosine 5'diphosphoribose (polyADP ribose) polymerization (PARP) inhibitor * Has had major surgery \<4 weeks prior to the first dose of study treatment (except for placement of vascular access) * Is expected to require any other form of antineoplastic therapy, while on study * Has received a live or live attenuated vaccine within 30 days before the first dose of study intervention; administration of killed vaccines is allowed * Has received colony-stimulating factors (e.g., granulocyte colony-stimulating factor \[GCSF\], granulocyte-macrophage colony-stimulating factor \[GM-CSF\] or recombinant erythropoietin) within 28 days prior to the first dose of study treatment * Is currently receiving either strong (phenobarbital, enzalutamide, phenytoin, rifampicin, rifabutin, rifapentine, carbamazepine, nevirapine and St John's Wort) or moderate (e.g. bosentan, efavirenz, modafinil) inducers of CYP3A4 that cannot be discontinued for the duration of the study * Is currently receiving either strong (eg, itraconazole, telithromycin, clarithromycin, protease inhibitors boosted with ritonavir or cobicistat, indinavir, saquinavir, nelfinavir, boceprevir, telaprevir) or moderate (eg. ciprofloxacin, erythromycin, diltiazem, fluconazole, verapamil) inhibitors of cytochrome P450 (CYP)3A4 that cannot be discontinued for the duration of the study * Is unable to interrupt aspirin or other nonsteroidal anti-inflammatory drugs (NSAIDs), other than an aspirin dose ≤1.3 grams per day, for at least 2 days before, during, and for at least 2 days after administration of pemetrexed * Is unable/unwilling to take folic acid, vitamin B12, and dexamethasone during administration of pemetrexed * Has received an investigational agent or has used an investigational device within 4 weeks prior to study treatment * The presence of uncontrolled, potentially reversible cardiac conditions, as judged by the investigator or has congenital long QT syndrome * Has a diagnosis of immunodeficiency or is receiving chronic systemic steroid therapy or any other form of immunosuppressive therapy within 7 days prior the first dose of study intervention * Has a known additional malignancy that is progressing or has required active treatment within the past 5 years with the exception of basal cell carcinoma of the skin, squamous cell carcinoma of the skin, superficial bladder cancer, or carcinoma in situ (excluding carcinoma-in situ-of the bladder) that have undergone potentially curative therapy * Has severe hypersensitivity (≥Grade 3) to study intervention and/or any of its excipients * Has an active autoimmune disease that has required systemic treatment in past 2 years * Has a history of (noninfectious) pneumonitis/interstitial lung disease that required steroids or has current pneumonitis/interstitial lung disease * Has an active infection requiring systemic therapy * Has a known history of human immunodeficiency virus (HIV) infection * Has a known history of Hepatitis B or known active Hepatitis C virus infection * Has active tuberculosis (TB; Mycobacterium tuberculosis) and is receiving treatment * Has a history or current evidence of any condition, therapy, laboratory abnormality or other circumstance that might confound the results of the study, or interfere with the participant's participation for the full duration of the study, such that it is not in the best interest of the participant to participate, in the opinion of the treating investigator * Is considered a poor medical risk due to a serious, uncontrolled medical disorder or nonmalignant systemic disease in the opinion of the treating investigator * Has a known psychiatric or substance abuse disorder that would interfere with the participant's ability to cooperate with the requirements of the study * Is unable to swallow orally administered medication or has a gastrointestinal disorder affecting absorption * Has had an allogenic tissue/solid organ transplant