Additional Study Information: The purpose of this study is to determine how safe the study drug, VTP-850, is in people with prostate cancer who have had initial treatment but whose prostate-specific antigen (PSA) levels have started to rise again. This study also aims to find the appropriate dose regimen of VTP-850 that can be given safely to people with prostate cancer. In addition, we want to see if VTP-850 brings about an immune response and if it has an effect on prostate cancer. VTP-850 is considered immunotherapeutic investigative drug, which means that it is meant to work by stimulating a person's immune system to react against their prostate cancer and kill prostate cancer cells. VTP-850 is an investigational vaccine for prostate cancer which means the study drug is not approved by Health Authorities including the United States Food and Drug Administration (FDA) for the treatment of prostate cancer. This will be the first time that VTP-850 will be given to humans.