This is a randomized double blind placebo-controlled study,with plans to include 5 additional U.S. centers in the near future. The primary goal of this study is to determine whether celecoxib has efficacy in elimination or reduction of recurrent disease in patients with RRP. Our secondary goals are to determine whether continued celecoxib is required to maintain response, to correlate response with select patient demographics and with plasma levels of celecoxib. The study design encompasses a 30-month period, which can be divided into three segments: