This is a multicentered, open label, randomized phase II trial of PROSTVAC or ipilimumab or the combination of PROSTVAC and ipilimumab as neoadjuvant therapy in patients with localized PC. Eligible patients will be randomized to PROSTVAC monotherapy (Arm A), ipilimumab monotherapy (Arm B), or combination therapy with both PROSTVAC and ipilimumab (Arm C), prior to RP. In arms A and C, PROSTVAC-V will be administered subcutaneously as the primary vaccine on Day 1, which will be followed 2 weeks later with a series of 2 PROSTVAC-F subcutaneous administrations, given 3 weeks apart. In arms B and C, ipilimumab will be administered twice, at a dose of 3mg/kg, 3 weeks apart. In the combination arm, ipilimumab administration will coincide with the PROSTVAC-F administration. In arm B, ipilimumab will begin on Day 1. In all three arms, RP will occur 21 days, or three weeks, following final treatment administration of PROSTVAC or ipilimumab. No further therapy will be administered on study following RP.