 This is an open-label, randomized phase II trial comparing treatment with a monoclonal antibody mAb drug immunoconjugate, SGN-15, administered weekly in combination with weekly Gemzar Gemcitabine to treatment with Gemzar alone. The primary objectives of this study are to determine the toxicity and safety profile of the combination of SGN-15 and Gemzar, to estimate the clinical response rate and to estimate the duration of response of this combination therapy administered to patients with advanced ovarian cancer, compared to treatment with Gemzar alone. 