The purpose of this study is to compare any good and bad effects of using aspirin after someone has completed the usual chemotherapy, surgery and or radiation therapy for breast cancer. Some studies have suggested that aspirin may lower the risk of breast cancer coming back, but others have not, so we do not know if aspirin will help decrease breast cancer recurrence. This study will evaluate whether patients taking aspirin once per day will have a lower rate of cancer recurrence than patients taking a placebo. A placebo is a tablet that looks like the study drug (aspirin), but contains no medication. This is explained further in the section under the section titled, What are the Study Groups.