Patients with ovarian cancer usually get the drugs carboplatin and paclitaxel as initial treatment. In many patients the tumor will shrink, or even disappear, after treatment with these drugs. But, unfortunately, the tumor will grow again in many patients. This trial will try to address the question: Can we delay the time, till the tumor grows again, by adding a 3rd drug to the standard therapy? To answer this question, patients will, by chance, either get the experimental drug enzastaurin or a "dummy pill" (placebo) during the chemotherapy and for up to 3 years after chemotherapy. Patients and physicians will not know, if a patient gets enzastaurin or placebo (double-blinded trial). After a predefined time, the treatment will be uncovered, and the number of patients with tumor growth at a specific time point will be compared between the two treatments.