The primary objective of this study is to determine if sulindac at a dose of 150 mg twice a day for 12 months reduces breast density in postmenopausal women at elevated risk of breast cancer when compared to a placebo control.

Inclusion Criteria:

1. Age ≤70 years
2. Subject must be postmenopausal.
3. Must have at least one healthy normal appearing breast (no prior diagnosis of invasive cancer, radiation or prosthetics). Prior biopsies are acceptable.
4. Must have dense breasts
5. Must be at elevated risk for developing breast cancer by abnormal pathological findings, family history, or genetic predisposition
6. A negative fecal occult blood test
7. Normal organ function
8. Hormonal therapy with aromatase inhibitors is allowed

Exclusion Criteria:

1. Daily aspirin or other daily anti inflammatory use.
2. Known intolerance to anti inflammatory.
3. Use of any selective estrogen receptor modulator therapy (e.g., tamoxifen, raloxifene) within past 12 months
4. Gastrointestinal, bleeding or coagulation, cardiovascular disorders.
5. Diabetes requiring insulin therapy.
6. Current regular smoker.
7. History of claustrophobia or inability to undergo imaging in a closed magnetic resonance imaging.
8. Cardiac pacemaker, cochlear implants, magnetic surgical clips or prostheses that would preclude MRI.
9. Uncontrolled hypertension.

There is no plan to share individual participant data to non study related researchers.