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The spatial configuration of the eukaryotic genome is organized and dynamic, providing the structural basis for regulated gene expression in living cells. In Drosophila melanogaster, 3D genome organization is characterized by the phenomenon of somatic homolog pairing, where homologous chromosomes are intimately paired from end to end. While this organizational principle has been recognized for over 100 years, the process by which homologs identify one another and pair has remained mysterious. Recently, a model was proposed wherein specifically-interacting “buttons” encoded along the lengths of homologous chromosomes drive somatic homolog pairing. Here, we turn this hypothesis into a precise biophysical model to demonstrate that a button-based mechanism can lead to chromosome-wide pairing. We test our model and constrain its free parameters using live-imaging measurements of chromosomal loci tagged with the MS2 and PP7 nascent RNA labeling systems. Our analysis shows strong agreement between model predictions and experiments in the separation dynamics of tagged homologous loci as they transition from unpaired to paired states, and in the percentage of nuclei that become paired as embryonic development proceeds. In sum, our data strongly support a button-based mechanism of somatic homolog pairing in Drosophila and provide a theoretical framework for revealing the molecular identity and regulation of buttons.