Low Dose Tamoxifen With or Without Omega-3 Fatty Acids for Breast Cancer Risk Reduction

Inclusion Criteria: * Age 45 - 74 * Postmenopausal female * Postmenopausal is defined as either * Prior removal of the ovaries, or if ovaries intact amenorrhea for \>= 12 months and not on any form of contraception, or * Amenorrhea for greater than 2 months with serum follicle-stimulating hormone (FSH) in postmenopausal range (\>= 25 IU/L). Women with ovaries and a prior hysterectomy or endometrial ablation \< age 55 must have a FSH \>= 25 IU/L. Women may be on vaginal low dose estrogen preparations for vaginal dryness. Women over age 50 with a levonorgestrel intrauterine device in place for 2 or more years and not planning removal in the next 6 month are also eligible if FSH \>= 25 IU/L * Note: FSH will be done at time of screening * Women with intact ovaries and uterus \< age 55 must have a negative pregnancy test prior to randomization * Overweight or obese (body mass index \[BMI\] \>= 25 kg/m\^2) * Note: BMI must be calculated within 28 days of randomization * Willing to undergo a fasting blood draw and non-fasting RPFNA with fixed and frozen aliquots sent to University of Kansas Medical Center (KUMC) * At increased risk of breast cancer per at least one of the following: * Personal medical history * History of atypical hyperplasia or lobular carcinoma in situ (LCIS) found on breast biopsy * History of unilateral ductal carcinoma in situ treated with unilateral mastectomy, lumpectomy, or local excision with or without radiation and this …