A Study to Evaluate the Effect of Gefapixant (AF-219/MK-7264) on Methacholine Hyper-reactivity in Participants With Asthma (MK-7264-009)

Inclusion Criteria: * Women of child-bearing potential (WOCBP) (i.e., women who are not surgically sterile, not having had hysterectomy, bilateral tubal occlusion or bilateral oophorectomy, or are not postmenopausal) must have a negative pregnancy test at Screening and prior to randomization. WOCBP must be using 2 forms of acceptable birth control method from Screening through the Follow-Up Visit. Acceptable birth control methods include (of which 2 must be used): * Established use of oral, injected or implanted hormonal methods of contraception * Intrauterine device (IUD) or intrauterine system (IUS) * Condom with spermicide * Diaphragm with spermicide * Double-barrier method (diaphragm for female participant and condom for male partner with spermicidal) satisfies the requirement for 2 forms of acceptable birth control. When in line with the preferred lifestyle of the participant, true and complete abstinence (not periodic abstinence) is acceptable. * Male participants with partners WOCBP (as defined in Inclusion No. 2) must use 2 methods of acceptable birth control with their partner, 1 of which must be a barrier method. Contraception must start from screening and continue until 3 months after last dose of study drug. * Non-smokers or former smokers, who stopped smoking 6 months prior to screening. Former smokers should not have a smoking history of more than 5 pack years (1 pack of 20 cigarettes per day over 5 years). * Physician documented history or diagnosis of asthma for at least 6 months prior to screening according to the Global Initiative in Asthma guidelines (GINA, 2012). * Requires the use of Short acting β2-agonist therapy only (≤ 8 puffs per day) for at least 4 weeks prior to screening and prior to randomization. Exclusion Criteria: * Has been hospitalized or attended the emergency department for an asthma attack in the 12 months prior to screening. * Exacerbation of asthma or lower respiratory tract infection during the 4 weeks before screening or prior to randomization. * Upper respiratory tract infection during the 4 weeks before screening or prior to randomization requiring treatment with antibiotics. * Inhaled or systemic corticosteroids (oral, intravenous, intramuscular) within 4 weeks prior to screening or prior to randomization. * Short-acting or long-acting antihistamines within 48hrs or 7 days, respectively, prior to screening. * Body mass index (BMI) \<18 kg/m2 or ≥ 35 kg/m2 at screening. * History of kidney/bladder stones (nephro/uro-lithiasis) within 5 years of screening. * History of conditions or disorders that predispose to nephrolithiasis, such as Type 1 renal tubular acidosis, cystinuria, gout, hyperparathyroidism, inflammatory bowel disease (i.e., ulcerative colitis and Crohn's disease), short bowel syndrome, or bariatric surgery. * History of concurrent malignancy or recurrence of malignancy within 2 years prior to Screening (not including participants with basal cell carcinomas or cervical carcinoma in situ that has been successfully treated surgically). * Personal or family history of congenital long QT Interval on ECG (QT) syndrome. * Presence of a cardiac pacemaker. * History of a diagnosis of drug or alcohol dependency or abuse within approximately the last 3 years. * Diagnosis of depression, psychosis, bipolar disorder, or schizoaffective disorder. * Participants with diabetes Type I or uncontrolled diabetes Type II or Glycosylated Hemoglobin (HbA1c) \> 8.0% at screening. * Any condition possibly affecting drug absorption e.g., gastrectomy, gastroplasty, any type of bariatric surgery, vagotomy, or bowel resection. * History of cutaneous adverse drug reaction to sulphonamides or signs or symptoms suggestive of anaphylaxis to sulphonamides. * Requiring concomitant therapy with prohibited medications at screening or prior to randomization. * Pregnant or breastfeeding woman. * Donation of sperm from Screening until 3 months after the last dose of study drug. * Male participants with pregnant female partners. * Treatment with an investigational drug within 30 days or five half-lives preceding the first dose of study medication or plans to take another investigational drug within 30 days of study completion. * Donation or loss of 400 mL or more of blood or donations of plasma within eight (8) weeks prior to initial dosing or longer if required by local regulation.