The major purpose of this research study is to better understand how therapy works on different patients. This study is being offered to patients with a diagnosis of advanced or metastatic breast cancer who have failed anthracycline based therapy. The investigators want to see the response of breast cancer cell when treated with Chloroquine used in combination with chemotherapy. Chemotherapy is an anti-cancer drug that is given through your vein. The chemotherapy used in this study is either Taxane (Paclitaxel) or Taxane-like drugs (Abraxane, Ixabepilone or Docetaxel).