This is a randomized double blind controlled study to determine if celebrex (celecoxib), a selective COX-2 inhibitor, can decrease the rate of recurrence in adult and pediatric patients with recurrent respiratory papillomatosis. All patients will be evaluated for disease severity at enrollment and at 3 month intervals for 30 months. After randomization, patients in the early treatment arm will begin celecoxib 6 months after enrollment. The delayed treatment arm will begin celecoxib 18 months after enrollment. All patients will receive celecoxib for 1 year. During the time that patients do not receive celecoxib, they will receive a placebo capsule with the same appearance. Follow-up visits will occur at three month intervals for the duration of the study.