This study will test the effectiveness of warfarin in patients with IPF. Approximately 256 patients will be randomized 1:1 to either warfarin or placebo. Patients will return at week 1 for a safety review and every 16 weeks for 48 weeks. The primary endpoint in the study is the time to either death, non-bleeding/non-elective hospitalization, or a drop of greater than 10% in forced vital capacity (FVC) from baseline.