We present a Chandra/Advanced CCD Imaging Spectrometer I-array observation of GRO J1744-28. We detected a source at a position of R.A. = 17h44m33.s09, decl. = -28°44'270 (J2000.0; with a 1 σ error of ~08), consistent with both ROSAT and interplanetary network localizations of GRO J1744-28 when it was in outburst. This makes it likely that we have detected the quiescent X-ray counterpart of GRO J1744-28. Our Chandra position demonstrates that the previously proposed infrared counterpart is not related to GRO J1744-28. The 0.5-10 keV luminosity of the source is (2-4) × 1033 ergs s-1 (assuming the source is near the Galactic center at a distance of 8 kpc). We discuss our results in the context of the quiescent X-ray emission of pulsating and nonpulsating neutron star X-ray transients.