Inclusion Criteria:

- Willing and able to give written informed consent

- Histologic diagnosis of adenocarcinoma of the prostate

- A PSA of > 0.2 ng/ml after 6-18 months of androgen suppression therapy, which may
consist of luteinizing hormone-releasing hormone (LHRH) agonist or antagonist alone
or the combination of an LHRH agonist or antagonist plus an antiandrogen, such as
bicalutamide; androgen suppression therapy will continue without interruption

- Radiographic evidence of regional or distant metastasis at the time of study
enrollment or at the time of diagnosis

- White blood cell (WBC) >= 2000/uL

- Absolute neutrophil count (ANC) >= 1000/uL

- Platelets >= 50 x 10^3/uL

- Hemoglobin >= 8 g/dL

- Creatinine =< 3.0 x upper limit of normal (ULN)

- Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) =< 2.5 *ULN for
patients without liver metastasis

- Bilirubin =< 3.0 x ULN, (except patients with Gilbert's Syndrome, who must have a
total bilirubin less than 3.0 mg/dL)

- No known active or chronic infection with human immunodeficiency virus (HIV),
hepatitis B, or hepatitis C; patients should be assessed for high risk behaviors that
may result in these infections, such as intravenous drug use or multiple sexual
partners; the assessment should be noted

- Eastern Cooperative Oncology Group (ECOG) =< 1

- Patients receiving any herbal product known to decrease PSA levels (i.e. saw palmetto
and prostate cancer [PC]-SPES), or any immunosuppressive dose of systemic or
absorbable topical corticosteroid (except prednisone up to 10 mg orally per [q] day,
or its equivalent), must discontinue the agent for at least 2 weeks prior to
screening; progressive disease must be documented after discontinuation of these
products

- Patients receiving bisphosphonate therapy must have been on stable doses for at least
4 weeks with stable symptoms prior to the first infusion with ipilimumab

- Total testosterone < 50 ng/ml, except in patients with prior orchiectomy, where
testosterone does not need to be measured; patients must continue their LHRH agonist
therapy throughout study duration

- Life expectancy >= 6 months; this must be documented

- Patients who are sexually active with a partner who could become pregnant are to use
an effective form of barrier contraception, such as condoms or a partner using oral
contraceptive pills; persons of reproductive potential must agree to use an adequate
method of contraception throughout treatment and for at least 8 weeks after
ipilimumab is stopped

- If a patient enters the trial on androgen suppression therapy (AST) that consists of
both an LHRH agonist and an oral antiandrogen, both agents should be continued
throughout the study; if an antiandrogen is stopped prior to study entry, it should
be stopped 4 weeks before for nilutamide and flutamide and 6 weeks before for
bicalutamide to ensure that a withdrawal phenomenon does not interfere with
interpretation of efficacy results

Exclusion Criteria:

- Prior history of pelvic radiation associated with significant radiation proctitis
within 12 months prior to planned first infusion of ipilimumab; for the purpose of
this protocol, radiation proctitis is defined as diarrhea that reached a level of
grade 2 or grade 3, that occurred within one month of radiation treatment, and that
was of 7 days duration or longer

- Radiation to any area of the body < 28 days prior to randomization

- Any other active malignancy with the exception of adequately treated basal or
squamous cell skin cancer, superficial bladder cancer or carcinoma in situ of the
cervix

- Autoimmune disease: Patients with a history of inflammatory bowel disease are
excluded from this study, as are patients with a history of symptomatic disease (eg,
rheumatoid arthritis, systemic progressive sclerosis [scleroderma], systemic lupus
erythematosus, autoimmune vasculitis [eg, Wegener's Granulomatosis]); motor
neuropathy considered of autoimmune origin (e.g. Myasthenia Gravis, Guillain-Barre
Syndrome); those with immune-mediated skin toxicity (i.e. Toxic Epidermal Necrolysis,
Stevens-Johnson Syndrome) will also be excluded

- Any underlying medical or psychiatric condition, which in the opinion of the
investigator will make the administration of ipilimumab hazardous or obscure the
interpretation of adverse events (AEs), such as a condition associated with frequent
diarrhea

- Any non-oncology vaccine therapy used for prevention of infectious diseases (for up
to 1 month before or after any dose of ipilimumab)

- A history of prior treatment with ipilimumab or prior cluster of differentiation
(CD)137 agonist or cytotoxic T-lymphocyte-associated protein 4 (CTLA-4) inhibitor or
agonist

- Concomitant therapy with any of the following: Interleukin (IL)-2,interferon, or
other non-study immunotherapy regimens; cytotoxic chemotherapy; immunosuppressive
agents (over the counter [OTC]/herbal/prescribed); immunostimulant agents, other than
the study agent; other investigational therapies; or chronic use of systemic
corticosteroids (greater than prednisone 10 mg orally per day, or its equivalent)

- Prisoners or patients who are compulsorily detained (involuntarily incarcerated) for
treatment of either a psychiatric or physical (i.e., infectious) illness