A Phase III Randomized Study of Exemestane Versus Placebo in Postmenopausal Women at Increased Risk of Developing Breast Cancer

* At increased risk of developing breast cancer, due to at least one of the following risk factors: * Gail score ≥ 1.66 * Age ≥ 60 years * Prior atypical ductal hyperplasia, lobular hyperplasia, or lobular carcinoma in situ on breast biopsy * Prior ductal carcinoma in situ (DCIS) treated with total mastectomy with or without tamoxifen (tamoxifen must have been completed ≥ 3 months prior to randomization) * No prior DCIS treated with lumpectomy with or without radiation * No prior invasive breast cancer * Not BRCA1 or BRCA2 carriers PATIENT CHARACTERISTICS: Previous: * 35 and over * Female * Postmenopausal, defined as one of the following: * over 50 years of age with no spontaneous menses for at least 12 months before study entry * 50 years of age or under with no menses (spontaneous or secondary to hysterectomy) for at least 12 months before study entry AND with follicle-stimulating hormone level within postmenopausal range * Underwent prior bilateral oophorectomy * No other malignancies within the past 5 years except adequately treated nonmelanoma skin cancer, curatively treated carcinoma in situ of the cervix, or other curatively treated solid tumors with no evidence of disease for ≥ 5 years * No uncontrolled hypothyroidism or hyperthyroidism * No major medical or psychiatric illness (including substance and alcohol abuse within the past 2 years) that would preclude study participation or compliance * Must be accessible for treatment and follow-up * Willing to complete quality of life questionnaires in either English or French Current: MAP.3 participants who were randomized to the exemestane arm, are currently receiving exemestane as part of the MAP.3 study and who have not completed 5 years of exemestane. OR MAP.3 study participants who were randomized to the placebo arm and who have either completed 5 years of study drug or who are still receiving placebo. Note: this applies only to centres that choose to allow placebo "cross-over". PRIOR CONCURRENT THERAPY: Previous: * More than 3 months since prior and no concurrent hormone replacement therapies * More than 3 months since systemic estrogenic, androgenic, or progestational agents * More than 3 months since prior and no concurrent hormonal therapies, including, but not limited to the following: * Luteinizing-hormone releasing-hormone analogs (e.g., goserelin or leuprolide) * Progestogens (e.g., megestrol) * Prolactin inhibitors (e.g., bromocriptine) * Antiandrogens (e.g., cyproterone acetate) * Selective estrogen-receptor modulators (e.g., tamoxifen, toremifene, or raloxifene) * No investigational drug within 30 days or 5 half lives prior to randomization * No concurrent endocrine therapy * No concurrent estrogens, androgens, or progesterones * Concurrent low dose (≤ 100 mg/day) prophylactic aspirin allowed * Concurrent bisphosphonates for prevention or treatment of osteoporosis allowed * No other concurrent medications that may have an effect on study endpoints Current: There are no prior concurrent therapy restrictions for the amended MAP.3 study.