  We present our successful Chandra program designed to identify, with
sub-arcsecond accuracy, the X-ray afterglow of the short GRB 111117A, which was
discovered by Swift and Fermi. Thanks to our rapid target of opportunity
request, Chandra clearly detected the X-ray afterglow, though no optical
afterglow was found in deep optical observations. The host galaxy was clearly
detected in the optical and near-infrared band, with the best photometric
redshift of z=1.31_{-0.23}^{+0.46} (90% confidence), making it one of the
highest known short GRB redshifts. Furthermore, we see an offset of 1.0 +- 0.2
arcseconds, which corresponds to 8.4 +- 1.7 kpc, between the host and the
afterglow position. We discuss the importance of using Chandra for obtaining
sub-arcsecond X-ray localizations of short GRB afterglows to study GRB
environments.
