An exchange gap in the Dirac surface states of a topological insulator (TI) is necessary for observing the predicted unique features such as the topological magnetoelectric effect as well as to confine Majorana fermions. We experimentally demonstrate proximity-induced ferromagnetism in a TI, combining a ferromagnetic insulator EuS layer with Bi(2)Se(3), without introducing defects. By magnetic and magnetotransport studies, including anomalous Hall effect and magnetoresistance measurements, we show the emergence of a ferromagnetic phase in TI, a step forward in unveiling their exotic properties.