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 the offset distribution of GRBs about their apparent hosts making extensive use of ground-based optical data from Keck and Palomar and space-based imaging from the Hubble Space Telescope. The offset distribution appears to be inconsistent with the coalescing neutron star binary hypothesis (and, similarly, black-hole--neutron star coalescences); instead, the distribution is statistically...

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