Chemotherapy plus trastuzumab (Herceptin) are standard treatments for breast cancer. There are circumstances where these treatments are given prior to surgery to reduce the size of the cancer and imptove the surgical outcome. In this trial, an oral drug called "vorinostat" will be given in combination with chemotherapy and trastuzumab. Vorinostat is a histone deacetylase (HDAC) inhibitor which is approved by the U.S. Food and Drug Administration for the treatment of a rare type of cancer involving the skin (cutaneous T cell lymphoma), but not for breast cancer. HDAC inhibitors work by unsilencing tumor suppressor genes and other genes in the cancer cells that are repressed; when the genes are turned back on by the drug, it leads to death of the cancer cells. HDAC inhibitors such as vorinostat have been shown to enhance the effects of chemotherapy and trastuzumab in experimental systems. The purpose of this trial is to determine the optimal dose of vorinostat to use in combination with standard chemotherapy plus trastuzumab, and to determine whether vorinostat enhances the effectiveness of standard chemotherapy plus trastuzumab.