 Ovarian cancer cannot grow without recruiting new blood vessels. Studies in humans have identified a novel cell population, termed vascular leukocytes VLCs. While VLCs are not cancer cells, they support the growth of ovarian cancer cells by stimulating the growth of new blood vessels which provide the cancer with nutrients. VLCs make a protein termed CD52. An antibody therapeutic, Alemtuzumab also know as Campath, that kills cells that make the CD52 protein has been successfully used to treat certain lymphomas a type of blood cell cancer that make CD52 protein. The purpose of this study is to determine if Alemtuzumab given subcutaneously under the skincan be safely given to patients with ovarian, fallopian, or primary peritoneal cancers to kill VLCs and determine if Alemtuzumab, by eliminating VLCs, can restrict tumor growth or increase response rates to chemotherapy given after the discontinuation of chemotherapy. 