We demonstrate, by both theory and experiment, the strain-induced self-organized formation of "quantum platelets," monolayer-thick islands of finite dimensions. They form at the early stage of heteroepitaxial growth on a substrate with regularly spaced steps, and align along the steps. In the direction perpendicular to substrate steps, the island position and spacing can be preselected through substrate miscut. Along the steps, the island size and density are controlled by self-organized growth.