The purpose of this study is to determine the effect of exemestane on the pharmacokinetics (PK) of entinostat and to determine the effect of entinostat on the PK of exemestane in patients with locally recurrent or metastatic estrogen receptor positive (ER+) breast cancer. Additionally, this study will evaluate the safety and tolerability of entinostat in combination with exemestane, and assess the effectiveness of entinostat in combination with exemestane in terms of best overall response and overall survival.