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We present the discovery of short GRB 080905A, its optical afterglow and host galaxy. Initially discovered by Swift, our deep optical observations enabled the identification of a faint optical afterglow, and subsequently a face-on spiral host galaxy underlying the GRB position, with a chance alignment probability of <1%. There is no supernova component present in the afterglow to deep limits. Spectroscopy of the galaxy provides a redshift of z=0.1218, the lowest redshift yet observed for a short GRB. The GRB lies offset from the host galaxy centre by ~18.5 kpc, in the northern spiral arm which exhibits an older stellar population than the southern arm. No emission lines are visible directly under the burst position, implying little ongoing star formation at the burst location. These properties would naturally be explained were the progenitor of GRB 080905A a compact binary merger.
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