Letrozole in Postmenopausal Women at Increased Risk for Breast Cancer

* Patients will be randomized into one of two study groups. Group 1 will receive letrozole and Group 2 will receive placebo. This is a double-blind trial so neither the patient or the doctor will know what treatment group they are assigned to. * If the patient is in Group 1 they will take letrozole tablets orally once a day with food for one year. Patients in Group 2 will take a placebo tablet orally once a day with food for one year. * Patients in both groups will also be given calcium tablets (500mg) and vitamin D tablets (400IU) once a day for one year. * After the initial screening visits, the patient will return to the clinic at 3, 6, 9 and 12 months (a total of up to 6 visits in the first year). There will also be two follow-up visits at 18 and 24 months. For the 3, 9 and 18 month visits, telephone contact instead of a clinic visit is allowed. * The following tests and procedures will be performed during these visits: evaluation of side effects; routine blood tests(6, 12, and 24 month visits); urine sample (6 and 12 month visits); complete physical exam including breast exam (12 and 24 month visits); mammogram (12 and 24 month visits); bone marrow density x-ray test (12 and 24 month visits); standard x-rays of the lower back and chest (12 month visit); and a questionnaire about how the patient is feeling (12 and 24 month visits). * The length of participation in this study is for 1 year of study treatment followed by 1 year of follow-up.