  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.
