Starting with the first detection of an afterglow from a short-duration hard-spectrum \gamma -ray burst ( SHB ) by Swift last year , a growing body of evidence has suggested that SHBs are associated with an older and lower-redshift galactic population than long-soft GRBs and , in a few cases , with large ( \mathrel { \hbox { \hbox to 0.0 pt { \hbox { \lower 4.0 pt \hbox { $ \sim$ } } } \hbox { $ > $ } } } 10 kpc ) projected offsets from the centers of their putative host galaxies .
Here we present observations of the field of GRB 060502B , a SHB detected by Swift and localized by the X-ray Telescope ( XRT ) .
We find a massive red galaxy at a redshift of z = 0.287 at an angular distance of 17.1 ^ { \prime \prime } from our revised XRT position .
Using associative and probabilistic arguments we suggest that this galaxy hosted the progenitor of GRB 060502B .
If true , this offset would correspond to a physical displacement of 73 \pm 19 kpc in projection , about twice the largest offset inferred for any SHB to date and almost an order of magnitude larger than a typical long-soft burst offset .
Spectra and modeling of the star-formation history of this possible host show it to have undergone a large ancient starburst .
If the progenitor of GRB 060502B was formed in this starburst episode , the time of the GRB explosion since birth is \tau \approx 1.3 \pm 0.2 Gyr and the minimum kick velocity of the SHB progenitor is v _ { kick,min } = 55 \pm 15 km s ^ { -1 } .