Inclusion Criteria: - Be a male >= 18 years of age - Have adenocarcinoma of the prostate - Currently receiving and must have had continuous therapy with Gonadotropin-releasing hormone (GnRH) monotherapy for at least 6 months before screening, with a serum testosterone of < 50 nanograms/deciliter (< 2.0 nanograms per milliliter) or have undergone surgical removal of the testicles with a blood testosterone level of < 50 nanograms per deciliter (<2.0 nanograms per millimeter) - Have rising Prostate Specific Antigen (PSA) after local therapy and treatment with GnRH monotherapy (defined as a PSA of greater than or equal to 10 nanograms/milliliter obtained at screening or PSADT (prostate-specific antigen doubling time) of < or equal to 6 months with a baseline PSA of greater than or equal to 2.0 nanograms/milliliter) - Have an Eastern Cooperative Oncology Group (ECOG) performance status less than or equal to 2 - Be capable of swallowing study agents whole as a tablet - Be willing/able to adhere to the prohibitions and restrictions specified in this protocol Exclusion Criteria: - Have prior or current evidence of local disease progression or metastatic disease as defined by modified response evaluation criteria in solid tumors (RECIST) criteria - Have received chemotherapy for treatment of castrate-resistant prostate cancer - Have a Prostate Specific Androgen Doubling Time (PSADT) of greater than 15 months - Subjects may not be currently receiving any antiandrogen therapy (e.g., bicalutamide, flutamide, or nilutamide) or have received agents having any CYP17 (a key enzyme in the production of testosterone) inhibitory activity (such as ketoconazole) or aminoglutethimide. For subjects previously treated with antiandrogen therapy, there must be documentation of at least 2 consecutive rising PSA values, obtained at least 2 weeks apart - For subjects previously treated with flutamide, at least 1 of the PSA values must be obtained 4 weeks or more after flutamide discontinuation - For subjects previously treated with bicalutamide or nilutamide, at least 1 of the PSA values must be obtained 6 weeks or more after antiandrogen discontinuation - Have an active infection or other medical condition that would contraindicate prednisone use - Have human immunodeficiency virus (HIV) or any other form of severe immunocompromise - Have uncontrolled hypertension - Have active hepatitis or chronic liver disease - Have clinically significant heart disease - Have poorly controlled diabetes - Have received an investigational therapeutic within 30 days of screening - Have partners of childbearing potential and are not willing to use a method of birth control with adequate barrier protection as determined to be acceptable by the principal investigator and sponsor during the study and for 13 weeks after last abiraterone acetate administration - Have had a malignancy excluding prostate cancer and nonmelanoma skin cancer (treated with no evidence of recurrence).