A Study of Prexasertib (LY2606368) in Platinum-Resistant or Refractory Recurrent Ovarian Cancer

Inclusion Criteria: * Women who have high-grade serous ovarian, primary peritoneal or fallopian tube cancer. * Cohorts 1 to 3: Have platinum-resistant disease and have documented test results assessing alterations in the BRCA1 and BRCA2 genes prior to receiving study treatment. * Cohort 1: Are BRCA negative and have received 3 or more prior lines of therapy. * Cohort 2: Are BRCA negative and have received less than 3 prior lines of therapy. * Cohort 3: Are BRCA positive and have previously received a PARP. * Cohort 4: Have primary platinum refractory disease. * Have adequate organ function. * Must be able and willing to undergo mandatory tumor biopsy. Exclusion Criteria: * Cohorts 1-3: Have previously received all of the following agents at any time in the platinum-resistant setting: gemcitabine, pegylated liposomal doxorubicin, and paclitaxel. * Have known central nervous system malignancy or metastasis. * Have previously participated in any study involving a checkpoint kinase 1 inhibitor or have hypersensitivity to the study drug or excipients. * Have at least one of the following: * history of abdominal fistula or gastrointestinal perforation * intra-abdominal abscess within last 3 months prior to the first dose of study drug * a radiographically confirmed bowel obstruction within 3 months prior to the first dose of study drug * Have a symptomatic human immunodeficiency virus infection or symptomatic activated/reactivated hepatitis A, B, or C (screening is not required). * Have a serious cardiac condition. * Have a history of prior radiotherapy to the whole pelvis. * Have chronic daily treatment with corticosteroids, excluding inhaled or topical steroids. * Have known factors that may increase the risk of infection while on study drug treatment. These may include, but are not limited to, an indwelling peritoneal catheter or open wounds. Catheters for vascular access are permitted.