The purpose of this study is to evaluate the allergen-induced late asthmatic response (LAR), as measured by maximal percent fall in forced expiratory volume in 1 second, in participants with stable mild atopic asthma after treatment with JNJ 40929837 as compared to placebo.

This is a multicenter (study conducted at multiple sites), randomized (the study medication is assigned by chance), double-blind (neither the physician nor participant will know which of the treatments a participant is receiving, but can access the information in case of an emergency), and crossover (method used to switch participants from one treatment arm to another in a clinical study) study. Approximately 18 participants will participate in the study. The study will consist of screening phase (30 days before the administration of study drug), treatment phase, and follow-up phase (2 weeks after the end of the last treatment period). Participants will be randomly assigned to receive JNJ 40929837, placebo, and montelukast. Each participant will receive all the 3 treatments (7 days per treatment) and each treatment will be separated by 14 days of wash-out period (no treatment). Safety evaluations will include assessments of adverse events, clinical laboratory tests, electrocardiogram, vital signs, and physical examination, which will be evaluated throughout the study. The maximum study duration for a participant will be approximately 51 days.

Inclusion Criteria: - Generally healthy - Have mild atopic asthma requiring no other treatment besides occasional short-acting beta-2-agonists - Have allergen-induced early asthmatic response of at least a 20 percent reduction in forced expiratory volume in 1 second (FEV1) and late asthmatic response of at least a 15 percent reduction in FEV1 during bronchial allergen challenge performed at screening - Females who are post menopausal, surgically sterilized, or practicing a highly effective method of birth control - Have an FEV1 at screening visit at least 75 percent of the predicted value - Have a history of asthma symptoms during exposure to indoor or outdoor allergens and a positive prick skin test done at the study site to dust mite, mixed grass pollen, or cat dander Exclusion Criteria: - Worsening of asthma or a respiratory tract infection within 6 weeks - HIV or Hepatitis B or C positive - Receipt of an investigational drug or use of an investigational medical device within the last month - Use of tobacco products of any kind currently or within 6 months - Have clinically significant abnormal physical examination, vital signs, or 12 lead electrocardiogram at screening as deemed appropriate by the investigator