We present small-angle neutron scattering data proving that, on the insulating side of the metal-insulator transition, the doped perovskite cobaltite La(1-x)Sr(x)CoO(3) phase separates into ferromagnetic metallic clusters embedded in a nonferromagnetic matrix. This induces a hysteretic magnetoresistance, with temperature and field dependence characteristic of intergranular giant magnetoresistance (GMR). We argue that this system is a natural analog to the artificial structures fabricated by depositing nanoscale ferromagnetic particles in a metallic or insulating matrix; i.e., this material displays a GMR effect without the deliberate introduction of chemical interfaces.