We show the existence of an N=1 supersymmetric vacuum in string theory whose observable sector has exactly the matter content of the MSSM without exotic particles and vector-like pairs of any type. This is done so by compactifying the E_8 x E_8 heterotic string on a Calabi-Yau threefold endowed with an SU(4) vector bundle which has been constructed after extensive search. In addition, we discuss the Yukawa couplings and Higgs mu-terms in this model.