We report on the results of observations of hard X-ray sources in the Galactic plane with the Chandra X-ray Observatory. The hard X-ray IGR sources were discovered by the INTEGRAL satellite, and the goals of the Chandra observations are to provide sub-arcsecond localizations to obtain optical and infrared counterparts and to provide constraints on their 0.3-10 keV spectra. We obtained relatively short, ~5 ks, observations for 20 IGR sources and find a bright Chandra source in INTEGRAL error circles in 12 cases. In 11 of these cases, a cross-correlation with optical and/or infrared source catalogs yields a counterpart, and the range of J-band magnitudes is 8.1-16.4. Also, in 4 cases, the Chandra X-ray spectra show evidence for absorbing material surrounding the compact object with a column density of local material in excess of 5x10^22 cm^-2. We confirm that IGR J00234+6141 is a Cataclysmic Variable and IGR J14515-5542 is an Active Galactic Nucleus (AGN). We also confirm that IGR J06074+2205, IGR J10101-5645, IGR J11305-6256, and IGR J17200-3116 are High Mass X-ray Binaries (HMXBs). Our results (along with follow-up optical spectroscopy reported elsewhere) indicate that IGR J11435-6109 is an HMXB and IGR J18259-0706 is an AGN. We find that IGR J09026-4812, IGR J18214-1318, and IGR J18325-0756 may be HMXBs. In cases where we do not find a Chandra counterpart, the flux upper limits place interesting constraints on the luminosities of black hole and neutron star X-ray transients in quiescence.
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