A second-order phase transition is characterized by spontaneous symmetry breaking. The nature of the broken symmetry in the so-called "hidden order" phase transition in the heavy fermion compound URu2Si2, at transition temperature T_h=17.5 K, has posed a long-standing mystery. We report the emergence of an in-plane anisotropy of the magnetic susceptibility below T_h, which breaks the four-fold rotational symmetry of the tetragonal URu2Si2. Two-fold oscillations in the magnetic torque under

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... ane field rotation were sensitively detected in small pure crystals. Our findings suggest that the hidden-order phase is an electronic "nematic" phase, a translationally invariant metallic phase with spontaneous breaking of rotational symmetry.