This study is a phase I/II open label clinical study in patients with platinum-resistant epithelial ovarian cancer. The Phase I part of the study will determine the dose of enadenotucirev to be recommended for further studies and will examine primarily the safety and tolerability but also the pharmacokinetics of administering enadenotucirev intraperitoneally. Once the dose of IP enadenotucirev to be used in combination with IV weekly paclitaxel has been determined, the phase II stage will begin as an open label dose expansion of that regimen. The phase II stage aims to determine whether intraperitoneal enadenotucirev has a risk benefit profile that supports further investigation in the treatment of patients with platinum-resistant epithelial ovarian Cancer.