The International Gamma-Ray Astrophysics Laboratory (INTEGRAL) satellite has detected in excess of 1000 sources in the ~20-100 keV band during its surveys of the sky over the past 17 years. We obtained 5 ks observations of 15 unclassified IGR sources with the Chandra X-ray Observatory in order to localize them, to identify optical/IR counterparts, to measure their soft X-ray spectra, and to classify them. For 10 of the IGR sources, we detect Chandra sources that are likely (or in some cases certain) to be the counterparts. IGR J18007-4146 and IGR J15038-6021 both have Gaia parallax distances, placing them at 2.5+0.5-0.4 and 1.1+1.5-0.4 kpc, respectively. We tentatively classify both of them as intermediate polar-type Cataclysmic Variables. Also, IGR J17508-3219 is likely to be a Galactic source, but it is unclear if it is a Dwarf Nova or another type of transient. For IGR J17118-3155, we provide a Chandra localization, but it is unclear if the source is Galactic or extragalactic. Based on either near-IR/IR colors or the presence of extended near-IR emission, we classify four sources as Active Galactic Nuclei (IGR J16181-5407, IGR J16246-4556, IGR J17096-2527, and IGR J19294+1327), and IGR J20310+3835 and IGR J15541-5613 are AGN candidates. In addition, we identified an AGN in the INTEGRAL error circle of IGR J16120-3543 that is a possible counterpart.