This is a randomized, placebo-controlled Phase I/II multi-center trial, of the safety and efficacy of Celecoxib in a cohort of 81 HNPCC subjects and gene carriers. The three proposed intervention arms are: Celecoxib (to be provided by Searle) will be administered at 200mg p.o. BID x 12 months or 400mg p.o. BID x 12 months vs. Placebo p.o. BID x 12 months. Assessment of endoscopic and tissue-based biomarker endpoints will be conducted at baseline and 12 months on study drug or placebo. Patients that present with polyps at baseline will undergo a month 4 endoscopy. Plasma drug trough samples for pharmacokinetic analyses will be collected at baseline and month 12. NCI-Chemoprevention Branch will coordinate the efforts and activities of all sites.