This is a double-blind randomized phase III study designed to determine if thalidomide can improve the efficacy of the luteinizing hormone releasing hormone (LHRH) agonist (leuprolide or goserelin) in hormone-responsive patients with a rising PSA after primary definitive therapy for prostate cancer. Patients with only a rising PSA will be randomized to LHRH agonist for six months followed by oral thalidomide 200 mg per day or placebo (phase A). At the time of PSA progression, an LHRH agonist will be restarted for six additional months. After six months, patients originally treated with thalidomide will be crossed over to placebo and patients originally treated with placebo will be crossed over to thalidomide and followed until PSA progression or the development of metastatic disease, whichever occurs first (Phase B). Additional information will be obtained on changes in the circulating levels of the following growth factors: basic fibroblast growth factor (bFGF), tumor necrosis factor (TNF), vascular endothelial growth factor (VEGF), and transforming growth factor beta (TGFbeta). Likewise we will monitor changes in testosterone and dihydrotestosterone (DHT) throughout the study. Neurological complications are the primary dose-limiting toxicity anticipated with chronic thalidomide administration.