This randomized phase III trial is studying glutathione to see how well it works in preventing peripheral neuropathy caused by paclitaxel and carboplatin in patients with ovarian cancer, fallopian tube cancer, and/or primary peritoneal cancer. Drugs used in chemotherapy work in different ways to stop the growth of cancer cells, either by killing the cells or by stopping them from dividing. Chemoprotective drugs, such as glutathione, may help prevent peripheral neuropathy caused by paclitaxel and carboplatin. It is not yet known whether glutathione is more effective than a placebo in preventing peripheral neuropathy.