Brief Summary: This pilot clinical trial studies how well degarelix acetate before and during radiation therapy works in treating patients with prostate cancer. Androgens can cause the growth of prostate cancer cells. Drugs, such as degarelix acetate, may lessen the amount of androgens made by the body. Radiation therapy uses high energy x-rays to kill tumor cells and shrink tumors. Giving degarelix acetate together with radiation therapy may work better in treating prostate cancer.

Detailed Description: PRIMARY OBJECTIVES: I. To evaluate the effect of neoadjuvant degarelix (degarelix acetate) on prostate dihydrotestosterone (DHT) and testosterone levels. SECONDARY OBJECTIVES: I. To determine the effect of degarelix acetate on androgen-regulated gene expression and apoptosis as assessed by immunohistochemistry, complementary deoxyribonucleic acid (cDNA) microarray analysis and reverse transcriptase (RT)-polymerase chain reaction (PCR). II. To determine the effect of degarelix acetate on follicle stimulating hormone (FSH) and FSH receptor expression in prostate cancer and surrounding microenvironment. OUTLINE: Patients receive degarelix acetate subcutaneously (SC) on day 1. Treatment repeats every 4 weeks for up to 6 courses. Beginning at week 15, patients also undergo standard external beam radiation therapy (EBRT) for 8.5 weeks.