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The various possibilities for the origin ("progenitors") of gamma-ray bursts (GRBs) manifest in differing observable properties. Through deep spectroscopic and high-resolution imaging observations of some GRB hosts, I demonstrate that well-localized long-duration GRBs are connected with otherwise normal star-forming galaxies at moderate redshifts of order unity. Using high-mass binary stellar population synthesis models, I quantify the expected spatial extent around galaxies of coalescing neutron stars, one of the leading contenders for GRB progenitors. I then test this scenario by examining...