A study to determine the effects of montelukast (MK-0476) on pediatric participants with chronic asthma compared with fluticasone. The primary hypotheses are that, over 24 weeks of treatment, montelukast will provide at least the same level of asthma control as inhaled fluticasone as measured by the percentage of days without asthma and that, over 24 weeks of treatment, daily administration of montelukast will be safe and well tolerated in children aged 6 months to 5 years with chronic asthma.