The objectives of this study are: 1) To determine the efficacy of the lipoxygenase inhibitor zileuton in reducing dysplasia of the bronchial epithelium in subjects at increased risk of lung cancer by virtue of pre-existing dysplasia. Participants with confirmed bronchial dysplasia will be randomized to zileuton or placebo for 6 months, followed by cross-over to the other arm of the study for an additional 6 months. 2) To determine the efficacy of zileuton in modulating intermediate biomarkers. 3) To evaluate the correlation between regression of bronchial dysplasia and modulation of biomarkers. 4) To evaluate the stability of a chemopreventive effect over 6 months following cessation of treatment and to evaluate the natural history of bronchial dysplasia over 6 months while participants are on placebo. 5) To evaluate the safety of zileuton in this cohort.