During spindle assembly, chromosomes generate gradients of microtubule stabilization through a reaction-diffusion process, but how this is achieved is not well understood. We have measured the spatial distribution of microtubule aster asymmetry around chromosomes by incubating centrosomes and micro-patterned chromatin patches in frog egg extracts. We then screened for microtubule stabilization gradient shapes that would generate such spatial distributions using computer simulations. Only a long-range sharply decaying microtubule stabilization gradient could generate aster asymmetries fitting the experimental data. We propose a reaction diffusion model that combines the chromosome generated Ran-GTP-Importin reaction network to a secondary phosphorylation network as a potential mechanism for the generation of such gradients. 10.1126/science.1161820