We report on 0.3-10 keV observations with the Chandra X-ray Observatory of eight hard X-ray sources discovered within 8 degrees of the Galactic plane by the INTEGRAL satellite. The short (5 ks) Chandra observations of the IGR source fields have yielded very likely identifications of X-ray counterparts for three of the IGR sources: IGR J14091-6108, IGR J18088-2741, and IGR J18381-0924. The first two have very hard spectra in the Chandra band that can be described by a power-law with photon indices of Gamma = 0.6+/-0.4 and -0.7(+0.4)(-0.3), respectively (90% confidence errors are given), and both have a unique near-IR counterpart consistent with the Chandra position. IGR J14091-6108 also displays a strong iron line and a relatively low X-ray luminosity, and we argue that the most likely source type is a Cataclysmic Variable (CV), although we do not completely rule out the possibility of a High Mass X-ray Binary. IGR J18088-2741 has an optical counterpart with a previously measured 6.84 hr periodicity, which may be the binary orbital period. We also detect five cycles of a possible 800-950 s period in the Chandra light curve, which may be the compact object spin period. We suggest that IGR J18088-2741 is also most likely a CV. For IGR J18381-0924, the spectrum is intrinsically softer with Gamma = 1.5(+0.5)(-0.4), and it is moderately absorbed, nH = (4+/-1)e22 cm-2. There are two near-IR sources consistent with the Chandra position, and they are both classified as galaxies, making it likely that IGR J18381-0924 is an Active Galactic Nucleus (AGN). For the other five IGR sources, we provide lists of nearby Chandra sources, which may be used along with further observations to identify the correct counterparts, and we discuss the implications of the low inferred Chandra count rates for these five sources.