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 \pm 0.2 arcseconds , which corresponds to 8.4 \pm 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 .