A Study of Gefapixant (MK-7264) in Japanese Adult Participants With Refractory or Unexplained Chronic Cough (MK-7264-038)

Inclusion Criteria: * Chest radiograph or computed tomography scan of the thorax not demonstrating any abnormality considered to be significantly contributing to the chronic cough or any other clinically significant lung disease in the opinion of the principal investigator or the sub-investigator. * Chronic cough for ≥ 4 months and a diagnosis of refractory or unexplained chronic cough. * Persistent cough, despite treatment in accordance with the latest guideline of cough from the Japanese Respiratory Society, cough is a burden to the participant, and needs further treatment. * If female, is not pregnant, not breast-feeding, and either is not a woman of childbearing potential or agrees to follow the contraceptive guidance. Exclusion Criteria: * Current smoker, or has given up smoking within 12 months of Screening. * History of upper or lower respiratory tract infection or recent clinically significant change in pulmonary status. * Has a history of chronic bronchitis. * Current use of an angiotensin converting enzyme inhibitor (ACEI) or has taken an ACEI within 3 months of Screening. * Estimated glomerular filtration rate (eGFR) \<30 mL/min/1.73 m\^2 OR ≥30 mL/min/1.73 m\^2 and \<50 mL/min/1.73 m\^2 at Visit 1 with unstable renal function (defined as a ≥50% increase of serum creatinine compared to a value obtained at least 6 months prior to Visit 1). * History of malignancy ≤ 5 years. * User of recreational or illicit drugs or has had a recent history (within the last year) of drug or alcohol abuse or dependence. * Systolic blood pressure \>160 mm Hg or a diastolic blood pressure \>90 mm Hg at Screening. * History of cutaneous adverse drug reaction to sulfonamide antibiotics or other sulfonamide-containing drugs. * Known allergy/sensitivity or contraindication to gefapixant. * Donated or lost ≥1 unit of blood within 8 weeks prior to the first dose of gefapixant. * Previously received gefapixant or is currently participating in or has participated in an interventional clinical study.