ABI-007 With Carboplatin as First-Line Therapy in Patients With Epithelial Ovarian, Primary Peritoneal, or Fallopian Tube Carcinoma

Inclusion Criteria: * Patients with a histological diagnosis of primary peritoneal carcinoma, fallopian tube or epithelial ovarian carcinoma (Stage III or IV) with either (optimal less than or equal to 1 cm) residual disease or suboptimal residual disease following initial appropriate surgery. * Patients with the following histologically confirmed types of ovarian cancer are eligible: serous cystadenocarcinoma, mucinous cystadenocarcinoma, clear cell adenocarcinoma, adenocarcinoma (unspecified), malignant Brenner's tumor, endometrioid adenocarcinoma, undifferentiated carcinoma, mixed epithelial carcinoma and transitional cell carcinoma. Patients with extraovarian papillary serous cystadenocarcinoma are eligible. * Patients who do not have measurable disease may be included and will be assessed for toxicity and progression-free survival only. Measurable disease is NOT required but when present will be followed to assess response. For patients to be evaluated for response of measurable disease, tumor must be greater than or equal to 2.0 cm with conventional computed tomography (CT) imaging or greater than or equal to 1.0 cm with spiral CT imaging. * No prior chemotherapy for ovarian cancer is permitted. * Patients must be entered no more than 12 weeks postoperatively. * ECOG performance status 0-2. * Age greater than or equal to 18 years. * Patient has the following blood counts at Baseline: * ANC greater than or equal to 1.5 x 10\^9 cells/L; * Platelets greater than or equal to 100 x 10\^9 cells/L; * Hemoglobin (Hgb) greater than or equal to 9 g/dL. * Patient has the following blood chemistry levels at Baseline: * AST (SGOT), ALT (SGPT) less than or equal to 2.5x upper limit of normal range (ULN); * Total bilirubin less than or equal to ULN; * Creatinine less than or equal to 1.5 mg/dL. * Peripheral neuropathy Grade 0 or 1 by National Cancer Institute Common Terminology Criteria for Adverse Events (NCI CTCAE). * It is assumed that almost all patients already had bilateral oophorectomy. However, if a female of childbearing potential, has a negative pregnancy test (within 72 hours of the first dose of study drug), the patient must agree to use an effective method to avoid pregnancy for the duration of the study. * Patients must have signed an approved informed consent and authorization permitting the release of personal health information. Exclusion Criteria: * Patients who have received any prior treatment, other than initial debulking surgery, for the cancer being treated in this study. Patients may have received adjuvant chemotherapy for localized breast cancer, if the therapy was completed greater than or equal to 3 years before registration in this study and if the patient remains free of recurrent or metastatic disease. * Patients who have received prior radiotherapy to any portion of the abdominal cavity or pelvis. Prior radiation for localized cancer of the breast, head and neck or skin is permitted if it was completed greater than or equal to 3 years before registration in this study and if the patient remains free of recurrent metastatic disease. * Concurrent immunotherapy or hormonal therapy for ovarian cancer. * Parenchymal brain metastases, unless documented to be clinically and radiographically stable for at least 6 months after treatment for the disease. * Serious intercurrent medical or psychiatric illness, including serious active infection (i.e. requiring antibiotics). * Patients with borderline or low malignant potential tumors. * History of other malignancy within the last 5 years, which could affect the diagnosis or assessment of ovarian cancer. * Patients who have received an investigational drug within the previous 3 weeks. * Patient is currently enrolled in a different clinical study in which investigational procedures are performed or investigational therapies are administered. Also, a patient may not enroll in such clinical trials while participating in this study. * Pregnant or nursing women. * Patients with unstable angina or those who have had myocardial infarction within the past 6 months. Patients with evidence of cardiac conduction abnormalities (e.g., bundle branch block, heart block) are eligible if their cardiac status has been stable for the 6 months prior to study entry. * Patients with prior hypersensitivity to both Taxol and Taxotere.