Inspired by experimental observations of spatially ordered growth hillocks on the (001) surfaces of natural graphite crystals, a mechanism for spatial organization in quantum dotself-assembly is proposed. The regular arrangement of steps from a screw dislocation-generated growth spiral provides the overall template for such ordering. An ordered array of quantum dots may be formed or nucleated from impurities driven to the step corners by diffusion and by their interactions with the spiral’s steps and kinks. Kinetic Monte Carlo simulation of a solid-on-solid model supports the feasibility of such a mechanism.