A phase-separation instability, resulting in the dewetting of thin SrTiO(3) films grown on Si(100) is shown by scanning transmission electron microscopy. Plan-view imaging of 1-nm thick, buried SrTiO(3) films was achieved by exploiting electron channeling through the substrate to focus the incident 0.2 nm beam down to a 0.04 nm diameter, revealing a nonuniform coverage by epitaxial SrTiO(3) islands and 2 x 1 Sr-covered regions. Density-functional calculations predict the ground state is a coexistence of 2 x 1 Sr-reconstructed Si and Sr-deficient SrTiO(3), in correspondence with the observed islanding.