Additional Study Information: This study will enroll participants with prostate cancer that were treated by removing the prostate or by giving radiation (or both), but whose blood prostate specific antigen (PSA) level is going up. PSA is produced by the prostate and other tissues, and when it goes up, it means that the prostate cancer is coming back. In this study, participants will take 4 enzalutamide or 4 placebo (contains no drug) capsules by mouth once each day. Enzalutamide is an androgen receptor inhibitor that works by blocking the action of the male hormone testosterone and other male hormones called androgens to slow down the growth of prostate cancer. Enazalutamide is approved in the United States (US) by the Food and Drug Administration (FDA) for men with advanced or metastatic castration resistant prostate cancer.