PS-341 Plus Carboplatin in Platinum and Taxane Resistant Recurrent Ovarian Cancer, Primary Peritoneal Cancer, and Fallopian Tube Cancer

Inclusion Criteria: * Patients must have histologically-confirmed ovarian cancer, primary peritoneal cancer, or fallopian tube cancer with advanced and/or metastatic disease. All patients must be considered platinum- and taxane- resistant. * Platinum resistance is defined as: 1. Progression of disease during platinum or taxane chemotherapy, or 2. Progression of disease within 6 months of completing platinum or taxane chemotherapy 3. Failure to achieve a complete response, with persistent macroscopic disease, after 6 cycles of chemotherapy, if the last two cycles had no measurable change in disease status * Patients may have had any number of prior chemotherapy regimens, except high dose chemotherapy an/or peripheral blood stem cell transplantation (high dose: higher than the standard doses of chemotherapy) * Patients must have measurable disease. * Zubrod performance status of \< 2. * Patients must give voluntary written informed consent before performance of any study-related procedure not part of normal medical care. * Adequate liver, renal and bone marrow function, defined as: * Absolute neutrophil count (ANC) \> 1.5 x 10\^9/L. * Platelets \> 100 x 10\^9/L * Total bilirubin \< 1.7 umol/L * Alanine transaminase (ALT) and aspartate transaminase (AST) \< 1.5 x Upper Limits of Normal (ULN) * Alkaline phosphatase \< 2.5 x ULN. * Serum creatinine \< 1.5 x ULN. Exclusion Criteria: * Chemotherapy within four weeks of first course of PS-341. (Patients may have been on hormonal therapy). * Patients who previously received high-dose chemotherapy (higher than the standard doses of chemotherapy) and/or peripheral blood stem cell transplantation. * Radiation therapy within four weeks of enrollment (excepting palliative XRT). * Patients not recovered from toxic effects of previous chemotherapy, radiation therapy, or antibody therapy. * Patients with \> Grade 2 peripheral neuropathy. * Surgery within four weeks of study enrollment. * History of severe hypersensitivity reaction to carboplatin * Electrocardiographic evidence of acute ischemia or new conduction system abnormalities. * Myocardial infarction within six months of enrollment. * Patients with brain metastases or central nervous system disease as evidenced by clinical symptoms. * History of other malignancy, except nonmelanoma skin cancer or carcinoma in-situ of the cervix, unless in complete remission and off all therapy for that disease for a minimum of 5 years. Chemotherapy given for prior cancers will not exclude patients from participating in this study. * Patients with previously documented human immunodeficiency virus (HIV) infection. HIV-positive patients are excluded from the study based on theoretical concerns regarding the effect of PS-341 on certain aspects of immune function. NF-KB is a critical T cell activation protein (including through CD40L/CD 154 stimulation) and also is involved in cytokine production. Because PS 341 effectively blocks NF-KB and therefore could reduce or block the ability of T lymphocytes and other immune cells to fight HIV, PS-341 should not be administered to HIV-positive patients. Additional experiments in animal models are being conducted to better elucidate the effects of PS-341 on HIV. * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, or cardiac arrhythmia. * Other serious medical or psychiatric illness that could, in the investigator's opinion, potentially interfere with the completion of treatment according to this protocol. * Patients who are pregnant, suspected to be pregnant, or breast-feeding. * Patients with a known hypersensitivity to PS-341, boron, or mannitol.