OUTLINE: This is a randomized, double-blind study. Participants are stratified by age (35 to 49 vs 50 to 59 vs over 59), race (black vs white vs other), history of lobular carcinoma in situ (yes vs no), prior hysterectomy (yes vs no), and estimated absolute risk of invasive breast cancer within 5 years (using the Gail model)(less than 2.0 vs 2.0-2.9 vs 3.0-4.9 vs 5.0 or greater). Participants are randomized to 1 of 2 arms.