Chromosomes are folded into cells in a nonrandom fashion, with particular genetic loci occupying distinct spatial regions. This observation raises the question of whether the spatial organization of a chromosome governs its functions, such as recombination or transcription. We consider this general question in the specific context of mating-type switching in budding yeast, which is a model system for homologous recombination. Mating-type switching is induced by a DNA double-strand break (DSB) at the locus on chromosome III, followed by homologous recombination between the cut locus and one of two donor loci (α and a), located on the same chromosome. Previous studies have suggested that in a cells after the DSB is induced chromosome III undergoes refolding, which directs the locus to recombine with α. Here, we propose a quantitative model of mating-type switching predicated on the assumption of DSB-induced chromosome refolding, which also takes into account the previously measured stochastic dynamics and polymer nature of yeast chromosomes. Using quantitative fluorescence microscopy, we measure changes in the distance between the donor (α) and loci after the DSB and find agreement with the theory. Predictions of the theory also agree with measurements of changes in the use of α as the donor, when we perturb the refolding of chromosome III. These results establish refolding of yeast chromosome III as a key driving force in switching and provide an example of a cell regulating the spatial organization of its chromosome so as to direct homology search during recombination.