At the beginning of the next menstrual period, women will begin the treatment phase of the study. They will receive random assignment to either UPA or COC at the study center and receive their first dose and a 4-week supply of study drug. During cycles 1 and 2 they will return to the study site every 2 weeks for assessment, blood draws and to receive the next cycle of study drug. During the third cycle, they will return to the study site twice weekly for more frequent testing and monitoring. Each cycle will be 28 days, corresponding to usual COC packaging. At day 75-77 of treatment women will undergo the second breast MRI, immediately followed by a biopsy of the contralateral breast to that biopsied at baseline. An end-of-study visit, including checking the incision site and a repeat assessment of acceptability of the MRI and biopsy to the participants, will occur about 7 days later. Participants will also be asked to rate their preference for an MRI versus a biopsy, were it possible to do a study with only one of these procedures.