Safety and Tolerability of Gefapixant (MK-7264) in Participants With Obstructive Sleep Apnea (MK-7264-039)

Inclusion Criteria: * International Classification of Sleep Disorders (ICSD-3) diagnosis of OSA, based on investigator's assessment of the obstructive sleep apnea (OSA) history and diagnostic interview which must include: Documented sleep study in the past that confirmed the OSA diagnosis without significant prior medical intervention. * Apnea-Hypopnea Index (AHI) ≥ 20 events/hour at screening. * No use of a positive airway pressure (PAP) device within the preceding 1 month or a dental appliance within the preceding 7 days prior to screening and is not allowed to use PAP or a dental appliance throughout the study (including washout intervals between treatment periods) and until the post-study visit. * A baseline oxygen saturation via pulse oximetry (SpO2) ≥ 94% at screening to ensure that carotid body response to hyperoxia is not impaired. * A body mass index (BMI) ≤ 35 kg/m\^2 at the pre-study (Screening 1) visit. * Judged to be in good health based on medical history, physical examination, vital sign measurements, and laboratory safety tests. * No clinically significant abnormality on electrocardiogram (ECG) * Contraceptive use by men and women should be consistent with local regulations regarding the methods of contraception for those participating in clinical studies. * A female participant is eligible to participate if she is not pregnant or breastfeeding, and is not a woman of childbearing potential (WOCBP) OR is a WOCBP and using an acceptable contraceptive method. * A WOCBP must have a negative highly sensitive pregnancy test (urine as required by local regulations) within 72 hours 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. * The investigator is responsible for review of medical history, menstrual history, and recent sexual activity to decrease the risk for inclusion of a woman with an early undetected pregnancy. * A consistent sleep-wake schedule that is not subject to any other unusual changes in sleeping routine (i.e., bedtimes and wake times do not vary more than 1-2 hours except on rare occasions). * Able to maintain sleep for at least 4 consecutive hours based on self-report. Exclusion Criteria: * Other than OSA, has evidence of another clinically significant, active pulmonary disorder such as bronchiectasis, emphysema, or asthma documented by history, physical examination, or chest x-ray. * A history within the past 6 months prior to the pre-study visit or current evidence of an unstable or clinically significant cardiovascular disorder, including but not limited to: acute coronary syndrome, unstable angina, congestive heart failure, cardiogenic syncope, cardiomyopathy, any symptomatic arrhythmia, orthostatic hypotension, uncontrolled hypertension, chronic kidney disease, kidney transplant * Abnormal pre-randomization laboratory values for alanine transaminase \> 1.5 x the upper limit of normal (x ULN), aspartate transaminase \> 1.5 x ULN, direct bilirubin \> 1.5 x ULN, serum creatinine of \> 2 mg/dL * A history or diagnosis of any of the following conditions, in the opinion of the investigator: narcolepsy (with or without cataplexy) or Idiopathic hypersomnia, circadian rhythm sleep disorder, parasomnia including nightmare disorder, sleep terror disorder, sleepwalking disorder, and rapid eye movement (REM) behavior disorder, periodic limb movement (PLM) disorder, restless legs syndrome, chronic insomnia * A WOCBP who has a positive urine or serum pregnancy test within 24 hours before the baseline 1 of study intervention. * A history of clinically significant or poorly-controlled endocrine, gastrointestinal, cardiovascular, hematological, hepatic, immunological, renal, respiratory, genitourinary, or major neurological (including stroke and chronic seizures) abnormalities or diseases. * Mentally or legally incapacitated, or has significant emotional problems at the time of pre-study screening * A history or current evidence of any condition, therapy, lab or ECG abnormality or other circumstances that might confound the results of the study, or interfere with the participant's participation for the full duration of the study. * Any history of a neurological disorder, including but not limited to seizure disorder (other than single episodes of childhood febrile seizures), stroke, transient ischemic attack, multiple sclerosis, cognitive impairment, or significant head trauma with sustained loss of consciousness within the last 10 years. * A history of significant multiple and/or severe allergies (e.g., food, drug, latex allergy), or has had an anaphylactic reaction or significant intolerability (i.e., systemic allergic reaction) to prescription or non-prescription drugs or food. * A history of anaphylaxis or cutaneous adverse drug reaction (with or without systemic symptoms) to sulfonamide antibiotics or other sulfonamide-containing drugs. * Positive for hepatitis B surface antigen, hepatitis C antibodies or HIV. * A history of cancer (malignancy) with some exceptions including adequately treated non-melanomatous skin carcinoma or carcinoma in situ of the cervix or; and other malignancies that have been successfully treated with appropriate follow up and therefore unlikely to recur for the duration of the study, in the opinion of the investigator and with agreement of the Sponsor (e.g., malignancies that have been successfully treated ≥ 10 years prior to the pre-study \[screening\] visit). * An estimated glomerular filtration rate (eGFR) \< 60 mL/min/1.73 m\^2 based on the Cockcroft-Gault (CG) Equation.