Inclusion Criteria:

1. Willing and able to give written informed consent;

2. Histologic Documentation: Histologic documentation of prostatic adenocarcinoma.
Patients with small cell, neuroendocrine, or transitional cell carcinomas are not
eligible. All eligible patients must have a known Gleason sum based on biopsy or TURP
at the time of registration.

3. Locally Resectable Disease: Patients must have disease (localized or locally
advanced) which is deemed by the surgeon to be resectable. Lymph node metastasis or
lymph nodes suspicious of harboring metastasis should be deemed surgically resectable
by the surgeon.

4. Determination of high-risk status: Patients must have either: 1) a Prostate biopsy
Gleason sum >/= 8 OR 2) PSA >/= 20.

5. Prior Treatment: No prior treatment for prostate cancer including prior surgery
(excluding TURP), pelvic lymph node dissection, radiation therapy, or chemotherapy.
Patients who have initiated leuprolide acetate within 1 week of signing consent will
be eligible.

6. Patients must be appropriate candidates for radical prostatectomy. Evidence of
underlying cardiac disease should be evaluated prior to enrollment to ensure that
patients are not at high risk of cardiac complications.

7. ECOG performance status of 0 or 1;

8. Required values for initial laboratory tests: a) WBC >/= 3000/uL; b) ANC >/= 1500/uL,
c) Platelets >/= 100 x 10^3/uL; d) Hemoglobin >/= 9 g/dL; e) Creatinine ULN; f) AST Syndrome, who must have a total bilirubin less than 3.0 mg/mL;

9. Men >/= 18 years of age

10. Patients must agree to practice barrier birth control methods while on therapy, prior
to surgery.

Exclusion Criteria:

1. Any other malignancy from which the patient has been disease-free for less than 5
years, with the exception of adequately treated and cured basal or squamous cell skin
cancer.

2. Autoimmune disease: Patients with a history of Inflammatory Bowel Disease (including
Crohn's disease and ulcerative colitis) are excluded from this study as are patients
with a history of autoimmune disease (e.g., rheumatoid arthritis, systemic
progressive sclerosis [scleroderma], Systemic Lupus Erythematosus, autoimmune
vasculitis [e.g., Wegener's Granulomatosis]).

3. Known HIV or chronic hepatitis.

4. Any underlying medical condition, which in the opinion of the Investigator, will make
the administration of study drug hazardous or obscure the interpretation of adverse
events, such as a condition associated with frequent diarrhea.

5. Patients who have had a history of acute diverticulitis, intra-abdominal abscess, GI
obstruction, abdominal carcinomatosis which are known risks factors for bowel
perforation, should be excluded from the study.

6. Any non-oncology vaccine therapy used for prevention of infectious diseases (for up
to one month prior to or after any dose of ipilimumab.

7. Concomitant therapy with any of the following: IL-2, interferon or other non-study
immunotherapy regimens; cytotoxic chemotherapy; immunosuppressive agents; other
investigation therapies; or chronic use of systemic corticosteroids (used in the
management of cancer or non-cancer-related illnesses);

8. Previous treatment with other investigational products within 30 days;

9. Previous enrollment in another MDX-010 (BMS-734016) clinical trial or prior treatment
with a CD137 agonist or CTLA-4 inhibitor or agonist

10. Concurrent use of 5-alpha-reductase inhibitors (finasteride, dutasteride).

11. Prisoners or patients who are compulsorily detained (involuntarily incarcerated) for
treatment of either a psychiatric or physical (e.g., infectious disease) illness must
not be enrolled in this study.